{ "query": "Please summarize the whole context. It is important that you include a summary for each file. All files should be included, so please make sure to go through the entire context", "namespace": "9b7a0d3b-f149-4977-879c-cf22ea8d011f", "messages": [], "stream": false, "language_level": "", "chat_channel": "", "language": "German", "tone": "neutral", "writing_style": "standard", "model": "gemini-1.5-flash", "knowledgebase": "ki-dev-large", "seed": 0, "client_id": 0, "all_context": true, "follow_up_for": null, "knowledgebase_files_count": 0, "override_command": "", "disable_clarity_check": true, "custom_primer": "", "logging": true, "query_route": "" } INITIALIZATION Knowledgebase: ki-dev-large Base Query: Please summarize the whole context. It is important that you include a summary for each file. All files should be included, so please make sure to go through the entire context Model: gemini-1.5-flash Use Curl?: ================================================== **Elapsed Time: 0.00 seconds** ================================================== ROUTING Query type: summary ================================================== **Elapsed Time: 1.84 seconds** ================================================== PRIMER Primer: You are Simon, a highly intelligent personal assistant in a system called KIOS. You are a chatbot that can read knowledgebases through the "CONTEXT" that is included in the user's chat message. Your role is to act as an expert at summarization and analysis. In your responses to enterprise users, prioritize clarity, trustworthiness, and appropriate formality. Be honest by admitting when a topic falls outside your scope of knowledge, and suggest alternative avenues for obtaining information when necessary. Make effective use of chat history to avoid redundancy and enhance response relevance, continuously adapting to integrate all necessary details in your interactions. Use as much tokens as possible to provide a detailed response. ================================================== **Elapsed Time: 0.41 seconds** ================================================== FINAL QUERY Final Query: CONTEXT: ########## File: VW%2010130_EN%281%29.pdf Page: 1 Context: # Volkswagen AG ## Machine Capability Investigation for Measurable Characteristics **VW 101 30** **Konzernnorm** Descriptors: machine capability investigation, capability index, quality capability, machine capability --- ## Contents 1. Purpose and scope .......................................................... 2 2. Principle of the machine capability investigation ............... 3 3. Theoretical principles .................................................... 4 3.1 Distribution models ................................................... 4 3.1.1 Normal distribution ........................................... 4 3.1.2 Absolute value distribution, type I ...................... 5 3.1.3 Type II absolute value distribution (Rayleigh distribution) .............................. 9 4. Determination of capability ............................................ 8 4.1 Determination of capability for defined distribution models .... 9 4.2 Determination of capability for undefined distribution models ... 16 3.3 Limit values of machine capability .............................. 18 5. Statistical tests ............................................................ 20 6. Carrying out a machine capability investigation ............... 21 6.1 Test equipment use .................................................. 24 6.2 Sampling ............................................................... 25 6.3 Special regulation for restricted MFI ......................... 25 6.4 Data analysis ............................................................. 25 6.4.1 Selection of the expected distribution model ....... 25 6.4.2 Test for outliers ................................................ 26 6.4.3 Take outliers out of the calculation of statistics ... 26 6.4.4 Test for change of the production location .......... 26 6.4.5 Test for deviation from the specified distribution model .... 26 6.4.6 Evaluation according to normal distribution .......... 26 6.4.7 Evaluation according to specified model ............. 26 6.5 Distribution-free evaluation ...................................... 27 7. Documentation ............................................................ 27 8. Results evaluation ......................................................... 29 9. Machine optimization .................................................... 29 10. Handling incapable machines ......................................... 30 11. Examples .................................................................... 30 12. Referenced standards .................................................... 33 13. Referenced literature ..................................................... 34 14. Keyword index ............................................................... 34 Image Analysis: 1. **Localization and Attribution:** - There is only one image on the page. 4. **Text Analysis:** - **Header:** - "Machine Capability Investigation for Measurable Characteristics" - "Volkswagen AG" - "VW 101 30" - "February 2005" - **Descriptors:** - "Descriptors: machine capability investigation, capability index, quality capability, machine capability" - **Table of Contents:** - Purpose and Scope: Page 2 - Principle of the machine capability investigation: Page 3 - Theoretical principles: Page 4 - Distribution models: Page 4 - Normal distribution: Page 4 - Absolute value distribution, type I: Page 5 - Type II absolute value distribution (Rayleigh distribution): Page 7 - Determination of capability: Page 8 - Determination of capability for defined distribution models: Page 9 - Determination of capability for undefined distribution models: Page 16 - Limit values of machine capability: Page 18 - Statistical tests: Page 20 - Carrying out a machine capability investigation: Page 21 - Test equipment use: Page 24 - Sampling: Page 24 - Special regulation for restricted MFI: Page 25 - Data analysis: Page 25 - Selection of the expected distribution model: Page 25 - Test for outliers: Page 26 - Take outliers out of the calculation of statistics: Page 26 - Test for change of the production location: Page 26 - Test for deviation from the specified distribution model: Page 26 - Evaluation according to normal distribution: Page 26 - Evaluation according to specified model: Page 26 - Distribution-free evaluation: Page 27 - Documentation: Page 27 - Results evaluation: Page 28 - Machine optimization: Page 29 - Handling incapable machines: Page 29 - Examples: Page 30 - Referenced standards: Page 33 - Referenced literature: Page 33 - Keyword index: Page 34 - **Footer:** - "Page 1 of 36" - "Confidential: All rights reserved. No part of this document may be transmitted or reproduced without prior permission of Standards Department of the Volkswagen Group. Please be aware that only oblations are standard via the B2B supplier platform 'www.vwgroupsupply.com'." 6. **Product Analysis:** - Title implies a focus on the machine capability investigation for measurable characteristics. - Document seems to be a detailed framework for evaluating and ensuring the quality of machine capabilities via statistical analysis and other methods. 10. **Contextual Significance:** - This document appears to be a detailed guideline intended for use within Volkswagen AG for evaluating machine capabilities. - The table of contents provides a structured framework of how machine capability can be systematically investigated and analyzed. - The text likely serves as a standard operating procedure or technical manual to ensure quality control in production processes. 11. **Metadata Analysis:** - Document created in February 2005. - Document identifier is "Klass.-Nr. 11 00 5." - The information is sectioned and enumerated, suggesting a well-organized manual or standard procedure. Overall, the attached visual content is an initial page of a comprehensive standard or guideline document designed to conduct, analyze, and ensure the quality and capability of machines used within Volkswagen AG. It includes a detailed table of contents offering a thorough insight into the structure and scope of the guideline. #################### File: VW%2010130_EN%281%29.pdf Page: 3 Context: # Principle of the Machine Capability Investigation Basically, different values of a considered characteristic result during the production of the same type of parts with the machine to be tested due to random influences. These characteristic values disperse around a location caused by systematic influences, depending on the production quality. Therefore, there is a test of how well the distribution of the characteristic values fits into the tolerance zone defined by the designer (Figure 1). The evaluation of this is expressed by the capability indexes \(C_{p}\) and \(C_{pk}\) (as in capability), whereby only the production dispersion is taken into consideration in the \(C_{p}\) value and the process location is additionally taken into consideration in the \(C_{pk}\) value. These statistics must be at least as great as the defined limit values in order to meet the requirement for a capable machine. To determine the capability indexes with respect to the considered characteristic, an adequately large random sample of produced parts (generally \(n = 50\)) is taken in direct sequence. So that essentially only the machine influence is recorded, the samples shall be taken under conditions that are as ideal as possible regarding the influence operators: material, human method, and environment. From this random sample, the location \(X_{0.135}\) and dispersion range limits \(X_{0.865}\) and \(X_{99.865}\) are estimated for the population of the characteristics values (theoretically infinite quantity) and compared to the tolerance zone \([G_{L}, G_{U}]\) (Figure 1). In this case, the dispersion range limits are specified in such a way that the percentage of characteristic values outside the dispersion range is \(p_{e} = 0.135\%\) on both sides. In addition, there is a test of whether the distribution of the characteristic values corresponds to an expected regularity. --- ### Figure 1 - Example of a Distribution of Characteristic Values Within a Defined Tolerance Zone | Characteristic Value | Frequency | |----------------------|-----------| | \(G_{L}\) | | | \(X_{0.135}\) | | | \(\mu\) | | | \(X_{99.865}\) | | | \(G_{U}\) | | *Note: The term characteristic value should not be confused with the term measured value, since in contrast to the first, the latter contains an uncertainty.* Image Analysis: ### Analysis of the Attached Visual Content #### 1. Localization and Attribution - **Image 1**: Located at the top of the page, consisting of a diagram and significant textual information. - **Image 2**: Located at the bottom of the page, consisting of a diagram labeled "Figure 1". #### 2. Object Detection and Classification - **Image 1**: Contains textual content discussing the principles of machine capability investigation. - **Image 2**: Contains a line graph depicting the distribution of characteristic values within a defined tolerance zone. #### 3. Scene and Activity Analysis - **Image 2**: The scene shows a bell-shaped curve representing the frequency distribution of characteristic values against the defined tolerance zone. Activities involve statistical analysis and quality control of produced parts. #### 4. Text Analysis - **Image 1**: - Title: "Principle of the machine capability investigation". - Main text discusses how different characteristic values are distributed during production. It emphasizes the importance of capability indices (\(c_m\) and \(c_{mk}\)) and how a sample of produced parts is analyzed to determine these indices. - **Image 2**: - Figure label: "Figure 1 - Example of a distribution of characteristic values within a defined tolerance zone". - In the diagram, annotation \(p_e = 0.135\%\) indicates the probability that a characteristic value falls outside the dispersion range on either side of the tolerance limits \(G_L\) and \(G_L\). - The axis labels indicate "Frequency" (vertical) and "Characteristic value" (horizontal), with specific points noted such as \(\mu\) (mean), \(X_{0.135%\) (0.135% quantile), and \(X_{99.865%}\) (99.865% quantile). #### 5. Diagram and Chart Analysis - **Image 2**: - The graph features a normal distribution curve (bell curve) with the defined tolerance range area shaded. - The horizontal axis represents the characteristic value, and the vertical axis represents frequency. - Key points on the graph include mean (\(\mu\)), lower tolerance limit (\(G_L\)), upper tolerance limit (\(G_L\)), and the respective quantiles \(X_{0.135%}\) and \(X_{99.865%}\). #### 7. Anomaly Detection - **Image 2**: There are no apparent anomalies within the diagram. The graph appears to be a standard illustration of a normal distribution within specified limits. #### 8. Color Analysis - **Image 2**: - The diagram uses black and white for clear representation. - The predominant colors are black (lines and text) and white (background), which emphasizes clarity and readability. #### 9. Perspective and Composition - **Image 2**: - The graph is presented in a front-facing view, typical for statistical illustrations. - The elements are arranged logically, with the curve centrally placed and annotations clearly marking key points and tolerance limits. #### 12. Graph and Trend Analysis - **Image 2**: - The normal distribution (bell curve) suggests that most characteristic values fall within the specified tolerance range. - The graph suggests that 0.135% of values are expected to fall outside the tolerance zone on each side, which may indicate a standard acceptable deviation in production quality. #### 13. Graph Numbers - **Image 2**: - \(p_e = 0.135\%\), \(G_L\), \(G_L\), \(\mu\), \(X_{0.135%}\), \(X_{99.865%}\). #### Additional Aspects - **Ablaufprozesse (Process Flows)**: The text in Image 1 details a process flow for determining the capability indexes based on sampling and analysis. - **Prozessbeschreibungen (Process Descriptions)**: The document describes the process for evaluating the distribution of characteristic values and the calculation of capability indexes (\(c_m\) and \(c_{mk}\)). - **Trend and Interpretation**: The bell curve in Image 2 indicates a typical distribution of characteristic values, suggesting the process is statistically controlled within the predefined tolerance zone. This analysis covers the key aspects you requested and provides a detailed examination of the attached visual content. #################### File: VW%2010130_EN%281%29.pdf Page: 4 Context: # Theoretical principles ## Distribution models The distribution of characteristic values can be described by a distribution model for most types of production characteristics. This means that most production characteristics with two-sided tolerance zones, e.g., length dimensions, diameters, and torques can be based on a normal distribution. In contrast, the variation behavior of production characteristics with upper limited tolerance zones can only be described by absolute value distributions of type I or type II. For example, the type I absolute value distribution can be used as the basis for the characteristic types parallelism and asymmetry, and the type II absolute value distribution can be used for the characteristic types position and coaxiality. ### Normal distribution The function of the probability density (density function for short) of a normal distribution that is shown graphically in Figure 2 is: $$ f_{X}(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^{2}}{2 \sigma^{2}}} $$ with the parameters mean value \( \mu \) and standard deviation \( \sigma \), that identify the location and width of a distribution, whereby the square of the standard deviation \( \sigma^{2} \) is identified as variance. ![Function of the probability density of a normal distribution](image_link) Figure 2 – Function of the probability density of a normal distribution *Illustrations, graphics, photographs, and flow charts were adopted from the original German standard, and the numerical notation may therefore differ from the English practice. A comma corresponds to a decimal point, and a period or a blank is used as the thousands separator.* Image Analysis: ## Detailed Analysis of the Visual Content ### 1. **Localization and Attribution** - **Image Placement on the Page:** - There is one image on the page. - **Numbering:** - The image is referred to as Image 1. ### 2. **Object Detection and Classification** - **Objects Identified:** - **Object Category:** Diagram - **Key Features:** - **Graph Components:** Probability density curve, x-axis, y-axis, turning points. - **Labels and Annotations:** μ (mean value), σ (standard deviation), probability density, characteristic value. ### 4. **Text Analysis** - **Detected Text:** - **Title:** "Theoretical principles" - **Section Number:** "3.1 Distribution models" - **Subsection:** "3.1.1 Normal distribution" - **Formula and Description:** ``` The function of the probability density (density function for short) of a normal distribution that is shown graphically in Figure 2 is: f_v(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-1}{2}(\frac{x - μ}{σ})^2} (1.1) ``` - Parameters: mean value (μ) and standard deviation (σ). - Note: Distribution variance is identified by the square of the standard deviation (σ²). - **Significance:** - Provides theoretical understanding of normal distribution. - Defines important statistical parameters and their roles in describing a normal distribution. ### 5. **Diagram and Chart Analysis** - **Chart Analysis:** - **Title:** "Figure 2 – Function of the probability density of a normal distribution" - **Axes:** - **Y-axis:** Probability density. - **X-axis:** Characteristic value. - **Scales and Labels:** μ - 4σ, μ - 3σ, μ - 2σ, μ - σ, μ, μ + σ, μ + 2σ, μ + 3σ, μ + 4σ. - **Key Insights:** - The probability density function (pdf) of the normal distribution is a bell-shaped curve. - Majority of the data falls within ±1σ (standard deviation) from the mean (μ). - From μ - 4σ to μ + 4σ, the probability density decreases symmetrically. - Turning Points: μ - σ and μ + σ mark where the concavity of the curve changes. - Points of interest: The areas under the curve at ±3σ from the mean encompass a large proportion of the distribution (~99.73%). ### 13. **Graph Numbers (for key annotations)** - **Data Points:** - Probability at Turning Points: p = 0.135% - Characteristic Values: Including μ - 4σ, μ - 3σ, μ - 2σ, μ - σ, μ, μ + σ, μ + 2σ, μ + 3σ, μ + 4σ. ### 6. **Product Analysis** - **Description:** N/A (No product is depicted). ### 7. **Anomaly Detection** - **Detection:** N/A (No anomalies detected). ### 8. **Color Analysis** - **Colors Detected:** - **Dominant Colors:** Black for text and lines. - **Impact on Perception:** Clear contrast aids in readability of the diagram and text. ### 9. **Perspective and Composition** - **Perspective:** Direct front view. - **Composition:** - Text is above the diagram with smooth separation for detailed explanations. - Diagram is centrally placed under relevant explanatory text providing logical flow. ### 10. **Contextual Significance** - **Contribution to Document:** - Provides a foundational understanding of statistical distribution models. - Essential in engineering and quality control settings to describe the behavior of production characteristics. ### 11. **Metadata Analysis** - **Date and Source:** - Page 4 of VW 101 30: 2005-02. - Emphasizes standards and guidelines likely related to vehicle production or similar processes. ### 12. **Graph and Trend Analysis** - **Trends:** - Symmetrical distribution around the mean. - Data clustering around mean μ with decreasing probability towards the distribution tails. ### **Ablaufprozesse and Prozessbeschreibungen** - **Processes:** - Describes the process of defining and understanding normal distribution in the context of statistical analysis. ### **Typen Bezeichnung, Trend, and Interpretation** - **Types and Trends:** - Distribution models, specifically normal distribution. - Clear pattern indicating central clustering of data and diminishing density outward. ### **Tables** - **Tables:** N/A (No tables are included). This detailed analysis covers the visual content comprehensively, interpreting the diagram, text, and overall context effectively for the reader's understanding. #################### File: VW%2010130_EN%281%29.pdf Page: 5 Context: The portion of the area below the graph in Figure 2 within a considered time interval can be interpreted as probability. The probability of finding a characteristic value \( x \) in a population that is at most as high as a considered limit value \( x_k \) is thus specified by the integral function (distribution function). For normal distribution, this is \[ F_{f_X}(x_k) = \int_{-\infty}^{x_k} f_{f_X}(x) \, dx \tag{1.2} \] where \[ \int_{-\infty}^{\infty} f_{f_X}(x) \, dx = 1 \tag{1.3} \] and \( f_{f_X}(x) \geq 0 \) for all values \( x \). With the transformation \[ u = \frac{x - \mu}{\sigma} \tag{1.4} \] produces the probability density of the standardized normal distribution \[ \phi(u) = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}u^2} \tag{1.5} \] and the distribution function \[ \Phi(x) = \int_{-\infty}^{u} \phi(u) \, du \tag{1.6} \] with the standard deviation \( \sigma = 1 \). ### 3.1.2 Absolute Value Distribution, Type I The type I absolute value distribution results from convolution of the density function of a normal distribution at the zero point, where the function values on the left of the convolution are added to those on the right. The density function and the distribution function of the type I absolute value distribution are thus \[ f_{f_B}(x) = \frac{1}{\sigma_N \sqrt{2\pi}} \left( e^{-\frac{(x - \mu_N)^2}{2\sigma_N^2}} + e^{-\frac{(x + \mu_N)^2}{2\sigma_N^2}} \right) \quad \text{for } x \geq 0 \tag{1.7} \] \[ F_{f_B}(x_k) = \Phi \left( \frac{x_k - \mu_N}{\sigma_N} \right) + \Phi \left( \frac{x_k + \mu_N}{\sigma_N} \right) - 1 \tag{1.8} \] where - \( \mu_N \): mean value of the original normal distribution that identifies a systematic zero point shift - \( \sigma_N \): standard deviation of the original normal distribution - \( \Phi \): distribution function of the standardized normal distribution Image Analysis: ### Detailed Examination: #### **Text Analysis:** - **Content Extraction and Significance:** - **Page Header:** - "Page 5" - "VW 101 30: 2005-02" - This indicates it is the fifth page of a document numbered VW 101 30, dated February 2005. - **Paragraph Content:** - **Section Title:** - "3.1.2 Absolute value distribution, type I". - **Explanation:** - The text explains the concept of probability density functions and distribution functions, focusing on normal distributions and absolute value distributions (Type I). It describes the mathematical formulations and transformations used. - **Equations:** - Several equations are provided to mathematically represent the concepts discussed: Equations (1.2) to (1.8). - Key equations include the integral representations of probability density functions and the use of standard normal distribution functions. - **Mathematical Notations:** - Various symbols and notations such as \( F_{n}(x_{g}) \), \( f_{n}(x)\), \( \Phi(u) \), and standard normal distribution formulas. - **Definitions and Variables:** - \( \mu_N \): Mean value of the original normal distribution. - \( \sigma_N \): Standard deviation of the original normal distribution. - \( \Phi \): Distribution function of the standardized normal distribution. #### **Contextual Significance:** - **Overall Relevance:** - This page serves an educational purpose, likely within a technical or statistical manual. It aims to educate readers on the mathematical foundations of probability distributions and their associated functions. It contributes detailed theoretical discussions relevant for applications in statistics, engineering, or quality control processes. #### **Diagram and Chart Analysis:** - **Absence of Diagrams and Charts:** - This document page does not contain any diagrams, charts, or graphical data. The analysis is purely textual and mathematical. #### **Process Descriptions:** - **Described Processes:** - The text details the process of deriving and using the probability density function for the standardized normal distribution. - It also describes the convolution process used to obtain the Type I absolute value distribution. #### **Perspective and Composition:** - **Textual Layout:** - The text is structured in a formal and precise layout, typical of academic or technical documentation. - Equations are numbered sequentially and embedded within the flowing explanatory paragraphs. #### **Localization and Attribution:** - **Single Image Analysis:** - This document comprises a single page and therefore is treated as 'Image 1'. - All text and mathematical content are attributed to this single image. ### Summary: The document page analyzed is a technical or academic text focused on probability distributions, specifically the normal distribution and Type I absolute value distribution. It includes detailed mathematical explanations and formulas, providing an in-depth educational resource for understanding these statistical concepts. The text layout is clear and formal, suitable for readers with some background in mathematics or statistics. This analysis showcases the document's role in conveying complex mathematical ideas with precision and clarity. #################### File: VW%2010130_EN%281%29.pdf Page: 6 Context: # Figure 3 - Density Function of the Type I Absolute Value Distribution with Different Zero Point Shifts Figure 3 shows density functions that result from convolution of the density of the normal distribution at different zero point shifts. ![Figure 3](image_link) ## Mean Value and Variance of the Type I Absolute Value Distribution The mean value and variance of the type I absolute value distribution are: \[ \alpha = x_N \left( \frac{ \xi_N }{ \sigma_N } - \frac{ \xi_N }{ \sigma_N } \right) \cdot \frac{2 \cdot \sigma_N}{\sqrt{2\pi}} \cdot e^{-\frac{ \xi_N^2 }{2}} \tag{1.9} \] \[ \sigma^2 = \sigma_N^2 + \kappa_N^2 \tag{1.10} \] For the case of a zero point shift \(\mu_N = 0\), the following results from (1.9) and (1.10): \[ \alpha = \frac{2 \cdot \sigma_N}{\sqrt{2\pi}} \tag{1.11} \] \[ \sigma^2 = \left( \frac{ t - 2 }{t} \right) \sigma^2_h \tag{1.12} \] As Figure 3 shows, with increasing zero point shift, the type I absolute value distribution approaches a normal distribution. Thus for the case \[ \frac{\alpha}{\sigma} \approx 3 \tag{1.13} \] the type I absolute value distribution can be replaced with a normal distribution with good approximation. Image Analysis: ### Analysis of the Visual Content: **Localization and Attribution:** - **Image Number:** Image 1 - **Position:** Singular image on the provided page. **Text Analysis:** - **Text Detected:** - **Page Header:** "Page 6 VW 101 30:2005-02" - **Title and Figure Description:** - "Figure 3 shows density functions that result from convolution of the density of the normal distribution at different zero point shifts." - "Figure 3 - Density function of the type I absolute value distribution with different zero point shifts" - **Mathematical Equations:** - Mean value and variance equations: \[ \alpha = x_{N} \left( \Phi \left( \frac{x_{N}}{\sigma_{N}} \right) - \Phi \left( \frac{- x_{N}}{\sigma_{N}} \right) \right) + 2 \cdot \sigma_{N} \cdot \frac{e^{\left( \frac{- x_{N}^2}{2 \cdot \sigma_{N}^2} \right)}}{\sqrt{2 \pi}} \] \[ \sigma^2 = \sigma_{N}^2 + x_{N}^{2} - \alpha^2 \] - For zero point shift \( \mu_N = 0 \): \[ \alpha = 2 \cdot \frac{\sigma_{N}}{\sqrt{2 \pi}} \] \[ \sigma^2 = \left( 1 - \frac{2}{\pi} \right) \cdot \sigma_{N}^2 \] - Approximation as a normal distribution: \[ \frac{\alpha}{\sigma} \approx 3 \] - **Paragraph:** - "As Figure 3 shows, with increasing zero point shift, the type I absolute value distribution approaches a normal distribution. Thus for the case \(\alpha / \sigma \approx 3\), the type I absolute value distribution can be replaced with a normal distribution with good approximation." **Diagram and Chart Analysis:** - **Chart Type:** Line graph - **Axes:** - **Y-Axis:** Probability density - **X-Axis:** Characteristic value - **Curves:** - Labeled \( \mu_N = 0 \) - Labeled \( \mu_N = 10_N \) - Labeled \( \mu_N = 20_N \) - Labeled \( \mu_N = 30_N \) - **Key Insight:** With increasing zero point shift (\(\mu_N\)), the distribution of the type I absolute value approaches that of a normal distribution. **Graph and Trend Analysis:** - **Trends:** - **Probability Density:** Changes as the characteristic value increases. - **Zero Point Shift Effects:** As the zero point shift (\(\mu_N\)) increases, the curve's shape transitions towards that of a normal distribution. - **Data Points & Observations:** - For \( \mu_N = 0 \), the graph shows a higher peak at lower characteristic values. - For \( \mu_N = 30_N \), the graph peak flattens out, indicating more spread out values, which aligns with the transition toward a normal distribution. **Color Analysis:** - **Dominant Colors:** Black and white. The lines representing different \(\mu_N\) values are black, while the background is white. - **Impact:** The high contrast makes the graph easy to read and interpret. **Perspective and Composition:** - **Perspective:** Straightforward view of the graph, head-on perspective. - **Composition:** The graph is centrally placed with titles, descriptions, and equations positioned around it. This arrangement aids in easy reference and comprehension. **Contextual Significance:** - **Overall Message:** The image contributes to explaining how the type I absolute value distribution, typically non-normal, can approximate a normal distribution with increasing zero point shift. - **Relevance:** This is likely part of a mathematical or statistical analysis document explaining different types of probability distributions and their properties. ### Summary: The provided image is a detailed graph illustrating how the density functions of a type I absolute value distribution change with different zero point shifts (\(\mu_N\)). Text explanations and mathematical equations help further elucidate the relationship between these shifts and the distribution's behavior. With increasing \(\mu_N\), the distribution approximates a normal distribution, a significant point emphasized both in the graph and supporting text. The document appears to be highly technical, targeting an audience with knowledge in mathematics or statistics. #################### File: VW%2010130_EN%281%29.pdf Page: 7 Context: # 3.1.3 Type II Absolute Value Distribution (Rayleigh Distribution) The type II absolute value distribution results from the vectorial values of the orthogonal components \( x \) and \( y \) of a two-dimensional normal distribution, where equal standard deviations are assumed for the components. This case is present for many production characteristics in the form of radial deviations from a considered point or a considered axis. The density function and the distribution function of the type II absolute value distribution are generally: \[ f_{B2}(r) = \frac{r}{2 \pi \sigma^2} e^{-\frac{1}{2 \sigma^2} \left( r^2 \right)} \int_{0}^{\frac{2 \pi \cos \alpha}{\sigma^2}} e^{-\frac{z^2}{2 \sigma^2}} d\alpha \quad \text{for } r \geq 0 \tag{1.14} \] \[ F_{B2}(r) = \int_{0}^{r} f_{B2}(r') \, dr' \tag{1.15} \] Where: - \( \sigma_h \): Standard deviation of the orthogonal components \( x \) and \( y \), from which the radial deviation \( r \) of a reference point or reference axis results. - \( z \): Eccentricity: distance between coordinate origin and frequency midpoint. Figure 4 displays density functions of the type II absolute value distribution that result in units of \( \sigma_h \) for different eccentricities. ![Figure 4 - Density functions of the type II absolute value distribution with different eccentricities](link_to_image) Mean value and variance of the type II absolute value distribution are: Image Analysis: ### Image 1 Analysis #### Object Detection and Classification: - The page contains text, equations, and a graph. - **Text:** The majority of the document is composed of paragraphs and section headers explaining the type II absolute value distribution (Rayleigh Distribution). - **Equations:** Mathematical equations and integrals are presented. - **Graph:** A plot with multiple curves is included to illustrate density functions for different eccentricities. #### Scene and Activity Analysis: - The page appears to be from a technical document or academic paper focusing on statistical distributions (Type II absolute value distribution). - The main activities include describing the underlying mathematical theory and illustrating it with a graph. #### Text Analysis: - **Title:** "Type II absolute value distribution (Rayleigh distribution)" - **Content:** The text provides a detailed explanation of the Type II absolute value distribution, using vector values of orthogonal components x and y of a two-dimensional normal distribution. It contains formulas, definitions, and a description of the graph. - **Equations:** Include density functions and integrals for the distribution. - Examples: - \(f_{BZ}(r) = \frac{r}{2 \pi \sigma_x \sigma_y} e^{- \left[ \frac{r^2(x^2 + y^2)}{2 \sigma_x^2 \sigma_y^2} \right]} \cdot 2 \pi \int_0^{2 \pi} e^{- \left[ \frac{2r \cdot cos \alpha}{2 \sigma_x^2 \sigma_y^2} \right]}d \alpha\) - \( F_{BZ}(r_g) = \int_0^{r_g} f_{BZ}(r)d r \) #### Diagram and Chart Analysis: - **Chart:** Figure 4 - "Density functions of the type II absolute value distribution with different eccentricities" - **Axes:** - x-axis: "Characteristic value" (ranges from 0 to 60) - y-axis: "Probability density" - **Curves:** - Four curves labeled as z = 0, z = 10σ_N, z = 20σ_N, and z = 30σ_N showing different distributions with varying eccentricities. - **Key Insight:** - As the eccentricity (z) increases, the peak of the probability density function shifts and changes shape, indicating how the distribution changes with different eccentricities. #### Contextual Significance: - The image is part of an academic paper or technical document discussing statistical distributions. - It contributes to the overall goal of explaining the characteristics and implications of the Type II absolute value distribution. #### Graph and Trend Analysis: - The graph illustrates how different eccentricities affect the density functions of the Type II absolute value distribution. Trends observed include: - Increasing eccentricity results in peak shifts of the probability density. - Higher eccentricity results in a broader distribution of values. #### Anomaly Detection: - No anomalies identified in the image. The content appears coherent and aligned with its purpose. Additional analysis of process flows, process descriptions, type designations, trend interpretations, and tables are not applicable as they are not present in this visual content. #################### File: VW%2010130_EN%281%29.pdf Page: 8 Context: # Page 8 VW 101 30: 2005-02 \[ \mu = \int_{0}^{\infty} f_{2}(r) \cdot r \, dr \tag{1.16} \] \[ \sigma^2 = 2\sigma_N^2 + z^2 - x^2 \tag{1.17} \] For an eccentricity \( z = 0 \), (1.14) and (1.15) density function and distribution function of the Weibull distribution, with the shape parameter value 2 yield \[ f_{2}(r) = \frac{r}{\sigma_H^2} \cdot e^{-\left(\frac{r}{\sigma_H}\right)^{2}} \tag{1.18} \] \[ F_{2}(y) = 1 - e^{-\left(\frac{y}{\sigma_H}\right)^{2}} \tag{1.19} \] and from them, in turn, mean value and variance \[ \mu = \sigma_H \cdot \sqrt{\frac{\pi}{2}} \tag{1.20} \] \[ \sigma^2 = \left(2 - \frac{\pi}{2}\right) \cdot \sigma_N^2 \tag{1.21} \] As Figure 4 shows, with increasing eccentricity, the type II absolute value distribution approaches a normal distribution. Thus for the case \[ \frac{\mu}{\sigma} \geq 6 \tag{1.22} \] the type II absolute value distribution can be replaced with a normal distribution with good approximation. ## 3.2 Determination of Capability The capability indexes \( C_p \) and \( C_{pk} \) indicate how well the production results comply with the tolerance zone of a considered characteristic. In this process, only the production dispersion is taken into consideration in the \( C_p \) value. The production location is taken into consideration by the \( C_{pk} \) value. Because of this, on the one hand, there can be an expression of what value is possible in an ideal production location and, on the other, a comparison of the two values makes it possible to express how much the production location deviates from the specified value. The higher the capability indexes determined, the better the production. There are different evaluation formulas, which have to be selected appropriately in the individual case, for determining the capability indexes. Since the determination of the capability indexes can only be carried out using random sample values, the results only represent estimates of the values for the population which are to be determined and are thus identified by a roof symbol[^1]. [^1]: The identification of the estimated capability indexes by a roof symbol is only important for understanding the theory, so they can be dispensed with during the evaluations in practice. Image Analysis: ### Analysis of the Attached Visual Content #### Image 1 1. **Localization and Attribution:** - **Image Number:** Image 1 - **Location:** Entire page 2. **Text Analysis:** - **Detected Text:** - Mathematical formulas and equations (e.g., \(\alpha = \int_0^r \bar{f}_{BZ}(r) \cdot r \cdot dr\) in Equation 1.16 and \( \sigma^2 = 2\bar{\sigma}_N^2 + z^2 - x^2 \) in Equation 1.17). - Description of the Weibull distribution and related concepts. - Discussion about production capability and evaluation formulas. - Section title **3.2 Determination of capability**. - Footnote discussing the importance of the estimated capability indexes symbolized by a roof symbol. - **Content Analysis:** - This section explains the mathematical definitions and properties of distributions, specifically the Weibull distribution and its related equations. - The text describes how to determine production capability indexes (\(c_m\) and \(c_{mk}\)) depending on the production location and tolerance zone. - The formulas underline the transition from Type II absolute value distribution to a normal distribution with increasing eccentricity. - The capability indexes (\(c_m\) and \(c_{mk}\)) are important for evaluating how well the production results adhere to the tolerance zone of a characteristic. These indexes consider both production dispersion and location deviation. 3. **Diagram and Chart Analysis:** - There are no explicit diagrams or charts present in this image; however, references to figures (e.g., Figure 4) and distribution transformations are mentioned. 4. **Contextual Significance:** - The content of this page is highly technical and it likely contributes to a broader discussion in a document or textbook related to statistical quality control or reliability engineering. - The mathematical and textual explanations about distribution types and production capability are crucial for understanding how well a manufacturing process performs relative to specified quality standards. - The detailed equations and explanations would be significant for those studying or working in fields involving statistical analysis, quality control, or manufacturing. 5. **Perspective and Composition:** - **Perspective:** - The perspective is straightforward, presenting the text and equations in a structured format typical of technical documents. - **Composition:** - The composition is formal and methodical, with clear sectioning and numbering of equations for easy reference. - The structured layout allows readers to follow the logical flow of the information presented. ### Key Insights: - The document discusses in detail the mathematical formulation and application of the Weibull distribution. - It transitions from theoretical distribution properties to practical application in determining manufacturing capabilities. - The capability indexes (\(c_m\) and \(c_{mk}\)) are critical for assessing the quality of manufacturing processes against specified tolerance zones. - The structure and composition provide clarity and facilitate the understanding of complex statistical concepts relevant to production quality. #################### File: VW%2010130_EN%281%29.pdf Page: 9 Context: # 3.2.1 Determination of capability for defined distribution models ## 3.2.1.1 Capability indexes For a production characteristic which is to be examined and whose random sample values are not in contradiction to a theoretically expected distribution model, the capability indexes are estimated in a manner appropriate to the respective case (see also examples 1 and 2 in Section 5) according to the following formulas: ### Capability indexes for characteristics with two-sided tolerance zones (according to DIN 55319, measuring method M4), e.g. for length dimension: \[ \hat{c}_m = \frac{G_o - G_u}{X_{99.865\%} - X_{0.135\%}} \] \[ \hat{c}_{mk} = \min \left( \frac{G_o - \bar{x}}{X_{99.865\%} - \bar{x}^2}, \frac{\bar{x} - G_u}{\bar{x} - X_{0.135\%}} \right) \] ### Capability indexes for characteristics with upper limited tolerance zone and natural lower limit value zero, e.g. for radial runout deviation: \[ \hat{c}_m = \frac{G_o}{X_{99.865\%} - X_{0.135\%}} \] \[ \hat{c}_{mk} = \frac{G_o - \bar{x}}{X_{99.865\%} - \bar{x}} \] ### Capability indexes for characteristics with lower limited tolerance zone only, e.g. for tensile strength: \[ \hat{c}_{mk} = \frac{\bar{x} - G_u}{\bar{x} - X_{0.135\%}} \] where - \(G_o, G_u\) : Upper and lower limiting value, respectively - \(\bar{x}\) : Estimated mean value - \(X_{0.135\%}, X_{99.865\%}\) : Estimated values for dispersion range limits (quantiles, below which the specified percentage \(p\) of measured values lie) Image Analysis: ### Detailed Examination of the Visual Content #### 1. Localization and Attribution: - **Image Identification:** - Single image on the page. - Identified as **Image 1**. #### 4. Text Analysis: - **Detected Text:** - Title: "3.2.1 Determination of capability for defined distribution models" - Subsection: "3.2.1.1 Capability indexes" - Descriptive text: Discusses the determination of capability indexes for production characteristics. - Formula descriptions and equations: - \[\hat{c}_{m} = \frac{G_o - G_u}{\hat{x}_{99.865\%} - \hat{x}_{0.135\%}}\] (Equation 2.1) - \[\hat{c}_{mk} = \text{min}\left\{\frac{G_o - z * \hat{x}_{99.865\%} - z * \hat{x}_{0.135\%}}{\hat{x}_{99.865\%} - z * \hat{x}_{0.135\%}}, \frac{z * \hat{G}_o}{z * \hat{x}_{0.135\%}}\right\}\] (Equation 2.2) - and several more equations for different types of capability indexes. - Terminology definitions: - \(G_o, G_u\): Upper and lower limiting values, respectively. - \(\hat{x}\): Estimated mean value. - \(\hat{x}_{0.135\%}, \hat{x}_{99.865\%}\): Estimated values for dispersion range limits for specific percentage points. #### 5. Diagram and Chart Analysis: - **Formula presentation:** - The image contains formulas (equations), but no graphical charts. - These formulas are methods for calculating capability indexes for various tolerance zones based on statistical measurements. #### 11. Metadata Analysis: - **Textual Metadata:** - Page number: "Page 9" - Document identifier: "VW 101 30: 2005-02" #### 12. Graph and Trend Analysis: - **Formulas and Relationships:** - Each formula corresponds to a specific calculation for capability indexes of production characteristics with different tolerance zones. - These mathematical relationships help in the determination of process capabilities in quality control. #### 13. Graph Numbers: - **Equation Numbers:** - Equations are clearly numbered (e.g., 2.1, 2.2, 2.3, 2.4, and 2.5), aiding in reference and context. ### Summary **Image 1** presents advanced statistical formulas for calculating capability indexes in the context of production quality control, as defined by specific tolerance zones. Each formula is detailed with precise variables and their definitions, emphasizing the importance of understanding the variations and limits in a production setting. The text is highly technical, suitable for professionals in quality control and manufacturing engineering, seeking to apply these concepts to ensure product and process reliability. There's a clear structure to the document section, starting from general determinations to specific cases, facilitating focused understanding of each type of capability index calculation. #################### File: VW%2010130_EN%281%29.pdf Page: 10 Context: # 3.2.1.2 Estimation of the statistics The statistics mean value \( \bar{x} \) and standard deviation \( \sigma \) of a population can be estimated, independently of the distribution model, from the measured values of a random sample according to expectation, by \[ \bar{x} = \frac{1}{n_e} \sum_{i=1}^{n_e} x_i \tag{2.6} \] \[ \sigma^2 = s^2 = \frac{1}{n_e - 1} \sum_{i=1}^{n_e} (x_i - \bar{x})^2 \tag{2.7} \] where - \( n_e = n - n_a \): effective random sample size - \( n \): defined random sample size - \( n_a \): number of outliers - \( x_k \): k-th characteristic value In the case of data to be evaluated in the form of a frequency distribution of classified measured values (e.g., from manual recordings (tally) in a class subdivision of the value range), the statistics \( \mu \) and \( \sigma \) can be estimated by \[ \bar{x} = \frac{1}{n_e} \sum_{k=1}^{K_{max}} a_k \cdot x_k \tag{2.9} \] \[ \bar{s} = \sqrt{\frac{1}{n_e - 1} \sum_{k=1}^{K_{max}} a_k \cdot (x_k - \bar{x})^2} \tag{2.10} \] where - \( x_k \): mean value of the k-th class - \( a_k \): absolute frequency of the measured values in the k-th class (without outliers) - \( K \): maximum number of measured value classes # 3.2.1.3 Estimation of the dispersion range limits The dispersion range limits depend on the distribution model and are estimated as follows: ## Dispersion range limits for normal distribution: If the normal distribution model is the fitting distribution model, the values \( \bar{x} \) and \( \sigma \) determined according to (2.6) and (2.7) or (2.9) and (2.10) respectively result as estimated values for the dispersion range limits \[ \hat{x}_{0.965} \quad \hat{x}_{0.0135} = \bar{x} \pm 3\sigma \tag{2.11} \] which, when used in formulas (2.1) and (2.2), result in the classical formulas for calculating the capability indexes (see also example 1 in Section 5). Image Analysis: ### Image Analysis #### Localization and Attribution - **Image 1:** The entire page appears to be a single image where text and mathematical formulas dominate. #### Text Analysis - **Text Content:** - **Section Heading:** "3.2.1.2 Estimation of the statistics" - **Explanatory Text:** The text explains methods to estimate statistics, like the mean value (x̅) and standard deviation (σ), using measured values from a random sample. - **Mathematical Formulas:** - \[ \hat{x} = x̅ = \frac{1}{n_e} \sum_{i=1}^{n_e} x_i \] (Equation 2.6) - \[ \hat{\sigma^2} = s^2 = \frac{1}{n_e - 1} \sum_{i=1}^{n_e} (x_i - x̅)^2 \] (Equation 2.7) - Descriptive variables n_e, n, n_A, x_i are explained. - **Frequency Distribution:** Methods involving frequency distribution of classified measured values and calculating mean and standard deviation. - Additional formulas: Equations (2.9) and (2.10) for estimating statistics using frequency distribution. - **Section 3.2.1.3:** Estimation of dispersion range limits. - **Dispersion Range Limits for Normal Distribution:** Formula: - \[ \hat{x}_{0.99865 \text{ to } 0.00135} = \hat{x} \pm 3\hat{\sigma} \] (Equation 2.11) #### Diagram and Chart Analysis - **Diagrams:** No diagrams or charts are present on the page. #### Scene and Activity Analysis - No specific scene or activity is depicted beyond the presentation of formulas and explanatory text. #### Metadata Analysis - No metadata information is provided or extracted from the image. #### Content Analysis - The content is highly technical and related to statistical estimations in quality control and process management, indicating an instructional or procedural document related to measurement systems or data evaluation. ### Conclusion The image is a technical document page explaining statistical methods for estimating mean value and standard deviation from a random sample, and how to estimate dispersion range limits based on normal distribution. The principal focus is on mathematical formulas and their explanation. #################### File: VW%2010130_EN%281%29.pdf Page: 11 Context: # Dispersion Range Limits of the Type I Absolute Value Distribution To determine the dispersion range limits for a type I absolute value distribution, the statistics \( \mu \) and \( \sigma \) are estimated according to formulas (2.6) and (2.7) or (2.9) and (2.10) respectively. For the case \( \frac{z}{\delta} < 3 \), the estimated statistics \( \mu \) and \( \sigma \) are used to estimate the parameter values \( \mu_N \) and \( \sigma_N \), to be determined for the type I absolute value distribution to be fitted, in the following manner: Equation (1.9) yields the function \[ \frac{\partial \hat{N}}{\partial N} = \psi_{N} \left( \frac{\hat{z}_{N}}{\partial N} - \frac{\hat{z}_{N}}{\partial N} \right) + \left( \frac{\hat{z}_{N}}{\partial N} - \frac{\hat{z}_{N}}{\partial N} \right) + 2 \left( \frac{ \partial \hat{z}_{A}}{ \partial N} \right)^3 \] With equation (1.10), this yields the following function \[ \frac{\partial \hat{N}}{\partial N} = \psi_{N} \left( \frac{\hat{z}_{N}}{\partial N} \right) \sqrt{1 + \left( \frac{\hat{z}_{N}}{\partial N} \right)^2} - \left( \psi_{N} \left( \frac{\hat{z}_{N}}{\partial N} \right) \right)^2 \] Equations (1.11) and (1.12) result in the condition \[ \frac{\partial \hat{N}}{\partial N} = \frac{2}{\sqrt{\pi}-2} = 1.3236 \] Under the condition (2.14), the parameter values to be determined for the type I absolute value distribution can be estimated using \[ \hat{\sigma}_N = \hat{\sigma} \left( \frac{1 + \left( \frac{z}{\hat{\sigma}} \right)^2}{1 + \left( \xi_{N} \left( \frac{z}{\hat{\sigma}} \right) \right)^2} \right) \] \[ \hat{z}_{N} = \xi_{B} \left( \frac{z}{\hat{\sigma}} \right) \cdot \hat{\sigma}_N \] where \( \xi_{B} \left( \frac{z}{\hat{\sigma}} \right) \) is the inverse function of (2.13). In the case where the ratio \( \frac{z}{\sigma} \) is lower than the limit value 1.3236 from condition (2.14) because of random deviations of the random sample statistics, the ratio \( \frac{z}{\sigma} \) is set to this limit value, at which the following parameter values result: \[ \hat{z}_{N} = 0 \] and according to formula (1.12) \[ \hat{\sigma}_N = \frac{\pi}{\sqrt{2}} \cdot \hat{\sigma} = 1.659 \cdot \hat{\sigma} \] Image Analysis: ## Analysis of the Attached Image ### Image 1 #### 1. Localization and Attribution - The document comprises a single page labeled as "Page 11". - Title: "Dispersion range limits of the type I absolute value distribution" - Document ID: VW 101 30: 2005-02 #### 4. Text Analysis - **Title:** "Dispersion range limits of the type I absolute value distribution" - Indicates the subject matter focuses on the statistical limits for type I absolute value distribution. - **Equations:** - **Equation (2.12):** Presents a function derived from Equation (1.9). - **Equation (2.13):** A resulting function utilizing the specified variables. - **Equations (1.11) and (1.12):** Lead to a resultant condition in Equation (2.14) where \( \frac{z}{\hat{\sigma}} = \frac{2}{\sqrt{\pi - 2}} = 1.3236 \). - **Equation (2.15):** Provides a method to estimate the parameter values. - **Equation (2.16):** Explains the parameter \( \xi_{\beta} \). - **Equation (2.17):** States the parameter values for specific conditions. - **Significant Mathematical Expressions:** - \(\mu_{X}\) and \(\sigma_{X}\): Parameters being determined for the type I absolute value distribution fit. - \(\hat{\sigma}\): Estimated standard deviation. - \(\frac{z}{\hat{\sigma}} = \frac{2}{\sqrt{\pi - 2}} = 1.3236\): Specifies a limitation based on Equation (2.14). - **Context and Explanation:** - The mathematical discourse explains how to calculate the dispersion range limits for the type I absolute value distribution. - Provides formulas for determining statistical values and conditions for setting certain limits when random deviations occur. #### 12. Graph and Trend Analysis - **Equations and Relationships:** - Parameter estimation relies on complex mathematical functions and equations to fit statistical data to a type I absolute value distribution. #### 13. Graph Numbers: - **Equations:** - (2.12) to (2.17) span various components of the formulae and their application under different conditions. #### 16. Ablaufprozesse (Process Flows): - Describes the quantitative process of deriving limits and distributing parameter estimations. #### 18. Prozessbeschreibungen (Process Descriptions): - Detailed steps on how to handle the scenario when the ratio \( \frac{z}{\hat{\sigma}} \) falls below the predefined limit. #### 20. Trend and Interpretation: - Interpretation of these mathematical relationships and equations shows how one can manage random deviations in sample statistics to stick within specified limits. ### Summary Statement This page of the document provides a series of mathematical derivations and equations relevant to determining the dispersion range limits for the type I absolute value distribution. The text includes detailed descriptions, equations, and conditions essential for understanding how to estimate statistical parameters accurately within predefined limits. The content is dense with mathematical formulae and processes, making it valuable for professionals or academics dealing with statistical distributions and parameter estimation techniques. #################### File: VW%2010130_EN%281%29.pdf Page: 12 Context: # VW 101 30: 2005-02 The connection between the parameter values \( \mu_H \) and \( \sigma_H \) of the type I absolute value distribution and the statistics \( \mu \) and \( \sigma \) is shown graphically in Figure 5, related to \( \sigma \). ![Figure 5 - Relative parameter values of the type I absolute value distribution in relationship to the relative location](figure5.png) For the fitted type I absolute value distribution, the dispersion range limits can then be determined numerically and their relationships with the relative location are shown in Figure 6. ![Figure 6 - Relative dispersion range limits of the type I absolute value distribution in relationship to the relative location](figure6.png) 1. Illustrations, graphics, photographs and flow charts were adopted from the original German standard, and the numerical notation may therefore differ from the English practice. A comma corresponds to a decimal point, and a period or a blank is used as the thousands separator. Image Analysis: ### Analysis of Attached Visual Content #### 1. **Localization and Attribution:** - **Image 1 (Top Graph):** - It is located at the upper part of the page, titled "Figure 5." - **Image 2 (Bottom Graph):** - It is located at the lower part of the page, titled "Figure 6." #### 2. **Object Detection and Classification:** - **Image 1:** - Objects: Graph, axes, data points, and labels. - **Image 2:** - Objects: Graph, axes, data points, and labels. #### 3. **Scene and Activity Analysis:** - **Image 1:** - Scene: A graph representing the relationship between relative distribution parameter (\(\sigma_{\lambda}\) / \(\sigma\), \(\sigma_{H}\) / \(\sigma\)) and relative location (\(\mu\) / \(\sigma\)). - Activity: Visualization of parameter values. - **Image 2:** - Scene: A graph illustrating the relative dispersion range limits (\(X_{99.865%}\) / \(\sigma\), \(X_{0.135%}\) / \(\sigma\)) in relation to the relative location (\(\mu\) / \(\sigma\)). - Activity: Visualization of dispersion range limits. #### 4. **Text Analysis:** - **Image 1:** - Titles and Labels: "Figure 5 - Relative parameter values of the type I absolute value distribution in relationship to the relative location," "Relative distribution parameter," "Relative location (\(\mu\) / \(\sigma\))," and data labels (\(\sigma_{\lambda}\) / \(\sigma\), \(\sigma_{H}\) / \(\sigma\)). - Significance: Indicates the correlation and trends for statistical parameter values. - **Image 2:** - Titles and Labels: "Figure 6 - Relative dispersion range limits of the type I absolute value distribution in relationship to the relative location," "Relative scatter range limit," "Relative location (\(\mu\) / \(\sigma\))," and data labels (\(X_{99.865%}\) / \(\sigma\), \(X_{0.135%}\) / \(\sigma\)). - Significance: Shows how the range limits change with the location parameter. #### 11. **Graph and Trend Analysis:** - **Image 1:** - Axes and Scales: - X-Axis: Labeled "Relative location (\(\mu\) / \(\sigma\))" ranging from 1.2 to 3.0. - Y-Axis: Labeled "Relative distribution parameter," ranging from 0.0 to 3.5. - Trends: As \(\mu/\sigma\) increases, both \(\sigma_{\lambda}/\sigma\) and \(\sigma_{H}/\sigma\) show distinct trends, with \(\sigma_{\lambda}/\sigma\) increasing more sharply than \(\sigma_{H}/\sigma\). - **Image 2:** - Axes and Scales: - X-Axis: Labeled "Relative location (\(\mu\) / \(\sigma\))" ranging from 1.2 to 3.0. - Y-Axis: Labeled "Relative scatter range limit," ranging from 0.0 to 7.0. - Trends: With increasing \(\mu/\sigma\), \( X_{99.865%} /\sigma \) and \( X_{0.135%}\) /\(\sigma\) exhibit varied dispersion range limits, indicating different behavior at the extremes of the distribution. #### 5. **Text Analysis:** - **Extracted Text:** - General Description: Provides interpretations of the graphs and explains the graphical representation of relationships for different parameter values. - Footnote: Explains terminological and notational differences in translations, specifying visualizations used in the document. #### 13. **Graph Numbers:** - **Image 1:** - Data Points: - X = 1.4, Y (\(\sigma_{\lambda}/\sigma\)) ≈ 1.9 - X = 1.4, Y (\(\sigma_{H}/\sigma\)) ≈ 0.6 - X = 3.0, Y (\(\sigma_{\lambda}\sigma\)) ≈ 2.9 - X = 3.0, Y (\(\sigma_{H}/\sigma\)) ≈ 1.7 - **Image 2:** - Data Points: - X = 1.4, Y ((\(X_{99.865%}\) / \(\sigma\))) ≈ 4.2 - X = 1.4, Y ((\(X_{0.135%}\) / \(\sigma\))) ≈ 2.0 - X = 3.0, Y ((\(X_{99.865%}\) / \(\sigma\))) ≈ 5.9 - X = 3.0, Y ((\(X_{0.135%}\) / \(\sigma\))) ≈ 3.1 #################### File: VW%2010130_EN%281%29.pdf Page: 13 Context: For direct determination of the statistics μ_N and σ_N from the statistics μ and σ, for \(1.3236 \leq \frac{σ}{d} < 3\) the following approximation can also be used as an inverse function of (2.13) with adequate precision (error related to less than 0.01): \[ \hat{σ}_{\bar{d}} = 1.64 \left( \frac{d}{\bar{d} - 1.3236} \right)^{0.268} + 0.634 \left( \frac{d}{\bar{d} - 1.3236} \right)^{1.105} \tag{2.18} \] In addition, the determination of the dispersion range limits for \(1.3236 \leq \frac{σ}{d} < 3\) is carried out directly with the use of the following approximation (error related to less than 0.02): \[ \hat{X}_{0.8696} = -2.47 \left( \frac{σ}{\bar{d} - 1.3236} \right)^{0.67} + 2.505 \left( \frac{σ}{\bar{d} - 1.3236} \right) + 5.3711 \tag{2.19} \] \[ \hat{X}_{0.1316} = 0.018 \left( \frac{σ}{\bar{d} - 1.3236} \right) + 0.0028 \] For \(\frac{σ}{d} \geq 3\) the calculation of the dispersion range limits is carried out according to formula (2.11). ## Dispersion Range Limits of the Type II Absolute Value Distribution: To determine the dispersion range limits for a type II absolute value distribution (see also example 2 in Section 5) first the statistics μ and σ are estimated according to formulas (2.6) and (2.7) or (2.9) and (2.10) respectively. For the case \(\frac{σ}{d} < 6\), the estimated statistics μ and σ are then used to estimate the parameter values z and σ_θ to be determined of the type II absolute value distribution to be fitted, in the following manner: Equations (1.14) and (1.16) yield the function: \[ \frac{σ}{\bar{d}} = \Psi_{g2} \left( \frac{σ}{d_N} \right) \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} \left( \frac{σ}{d_N} \right)^2} \int_0^{z} v^2 e^{- \frac{1}{2} v^2} \frac{2}{σ} e^{-\frac{z^2}{2}} dα \, dv \tag{2.20} \] where \[ v = \frac{σ}{d_N} \tag{2.21} \] With equation (1.17), this yields the following function: \[ \hat{σ} = \Psi_{g2} \left( \frac{σ}{d_N} \right) \frac{\Psi_{g2} \left( \frac{σ}{d_N} \right)}{\sqrt{2} \left( \frac{σ}{d_N} \right)^2 - \Psi_{g2} \left( \frac{σ}{d_N} \right)} \tag{2.22} \] Equations (1.20) and (1.21) result in the condition: \[ \frac{σ}{\bar{d}} = \frac{\pi}{4 - π} = 1.9131 \tag{2.23} \] Image Analysis: 1. **Localization and Attribution:** - The document contains one image, located in the entirety of the page. It will be referred to as **Image 1**. 2. **Object Detection and Classification:** - **Image 1** contains textual content, mathematical equations, and notations. 3. **Text Analysis:** - **Image 1** contains the following notable text segments: - **Top Header**: "Page 13 / VW 101 30: 2005-02" - **Section Title**: "For direct determination of the statistics μ_N and σ_N... (error related to less than 0.01)" - **Equations**: A total of eight equations, labeled (2.18) to (2.23). - **Subsection Heading**: "Dispersion range limits of the type II absolute value distribution" - **Additional text** discussing the process of determining dispersion range limits and related calculations. - Significant Textual Content: - **Equations (2.18) - (2.23)** present various mathematical models and formulas related to the dispersion range limits and calculations of statistics μ_N and σ_N. - **Contextual Explanation**: Details regarding error approximation and calculations for different scenarios based on the parameter range of ξ/δ. 4. **Diagram and Chart Analysis:** - There are no diagrams or charts in this image. 5. **Product Analysis:** - There are no products depicted in this image. 6. **Anomaly Detection:** - No noticeable anomalies or unusual elements are present in the textual and mathematical content. 7. **Color Analysis:** - The image is in black and white, adding a professional and formal look. 8. **Perspective and Composition:** - The perspective is a straight-on view typical for document scans. - The composition is methodical and neatly organized with headings, subheadings, and equations in sequential order. 9. **Contextual Significance:** - The text and equations are part of a technical document concerning statistical methods and distribution calculations. It contributes to explaining complex statistical procedures and their precise determination, likely intended for an audience with a background in statistics or related fields. 10. **Graph and Trend Analysis:** - No graphs are present in this image. 11. **Tables:** - There are no tables included in this image. 12. **Additional Aspects:** - **Ablaufprozesse (Process Flows)**: The process described involves calculating statistical parameters and dispersion limits. - **Prozessbeschreibungen (Process Descriptions)**: Detailed steps for determining statistics μ_N and σ_N and dispersion range limits are provided. - **Typen Bezeichnung (Type Designations)**: The document references "type II absolute value distribution," indicating a particular statistical distribution type. - **Trend and Interpretation**: No specific trends are described, but the detailed equations and explanations suggest a robust theoretical approach to statistical analysis. #################### File: VW%2010130_EN%281%29.pdf Page: 14 Context: # Page 14 VW 101 30: 2005-02 Under the condition (2.23), the parameter values to be determined of the type II absolute value distribution can be estimated using $$ d_N = \bar{d} \cdot \left[ 1 + \frac{z^2}{2 \left( \frac{\sigma}{\bar{d}} \right)^2} \right] $$ (2.24) $$ \bar{z} = \frac{\sigma}{\bar{d}} \cdot d_N $$ (2.25) where $$ \epsilon_{Z2} \left( \frac{\bar{z}}{\bar{d}} \right) : \text{inverse function of (2.22)} $$ In the case where the ratio $\frac{\bar{z}}{d}$ is lower than the limit value 1.9131 from condition (2.23) because of random deviations of the random sample statistics, the ratio $\frac{\bar{z}}{d}$ is set to this limit value, at which the following parameter values result: $$ \bar{z} = 0 \quad \text{and according to formula (1.21)} $$ $$ d_N = \frac{2}{\sqrt{4 - \pi}} \cdot \bar{d} = 1.526 \cdot \bar{d} $$ (2.26) The connection between the parameter values $z$ and $d_N$ of the type II absolute value distribution and the statistics $\mu$ and $\sigma$ is shown graphically in Figure 7, related to $\sigma$. ![Figure 7 - Relative parameter values of the type II absolute value distribution in relationship to the relative location](figure7.png) 1) Illustrations, graphics, photographs, and flow charts were adopted from the original German standard, and the numerical notation may therefore differ from the English practice. A comma corresponds to a decimal point, and a period or a blank is used as the thousands separator. Image Analysis: ### Comprehensive Examination of the Provided Visual Content #### 1. Localization and Attribution - **Page:** Single page (Page 14) - **Image Numbering:** - **Image 1:** Positioned at the bottom of the page #### 3. Scene and Activity Analysis - **Text Analysis:** - The page contains mathematical equations and explanations related to statistical distributions. - The text explains conditions, parameter values, and formulas concerning the type II absolute value distribution. #### 4. Text Analysis - **Extracted Text:** - The text includes formulas, explanations, and theoretical derivations. - Key extracted formulae: - \(\sigma_N = \bar{\sigma} \cdot \left(1 + \left(\frac{\hat{z}}{\bar{\sigma}}\right)^2\right) \cdot \frac{1}{\sqrt{2 + \left(\xi_{BZ} \left(\frac{\hat{z}}{\bar{\sigma}}\right)\right)^2}}\) (2.24) - \(\hat{z} = \xi_{BZ} \left(\frac{\hat{\sigma}}{\bar{\sigma}}\right)^2 \cdot \sigma_N\) (2.25) - **Significance:** - The equations detail statistical methods to determine parameters of the type II absolute value distribution. The definitions and derived values are significant for statisticians and researchers analyzing random samples. #### 5. Diagram and Chart Analysis - **Image 1 (Figure 7):** - **Description:** - Title: "Relative parameter values of the type II absolute value distribution in relationship to the relative location." - **Axes:** - **X-axis:** Labeled as "Relative location μ / σ" with a range from 1.5 to 6.0 - **Y-axis:** Labeled as "Relative distribution parameter" with a range from 1 to 7 - **Graph Features:** - Two curves representing \( \sigma_N / \sigma \) and \( Z / \sigma \) - From the legend, \( Z / \sigma \) increases more steeply compared to \( \sigma_N / \sigma \) - **Insights:** - The graph visualizes the relationship between parameter values Z and σN of type II absolute value distributions related to the ratio μ / σ. - The curves indicate how these relative parameters change with varying values of relative location. #### 7. Anomaly Detection - **Anomalies:** - None detected. #### 8. Color Analysis - **Dominant Colors:** - The page predominantly uses black and white, common for academic and technical documents. - The graph lines and labels maintain a simple, clear distinction to ensure readability. #### 9. Perspective and Composition - **Perspective:** - The perspective is straightforward, primarily for academic review purposes. - **Composition:** - The composition aligns text explanations with corresponding visual aids (graph) to facilitate understanding. - The mathematical text is structured in paragraphs with referenced equations for logical flow. #### 12. Graph and Trend Analysis - **Trends in Figure 7:** - The parameter \( \sigma_N / \sigma \) remains above 1 and increases slightly as \( μ / σ \) increases. - The parameter \( Z / \sigma \) shows a steeper linear growth with increasing \( μ / σ \). - **Interpretations:** - Both parameters suggest increasing trends as the relative location parameter grows, indicating a relationship between statistical dispersion and location metrics. #### 13. Graph Numbers - **Data Points:** - Specific values are not tagged along the curves. The data interpretation relies on visual inference. #### Additional Aspects - **Process Flows, Process Descriptions, Type Designations, and Tables:** - Not applicable or absent in this visual content. ### Summary The provided visual content primarily revolves around statistical analysis and parameter determination for the type II absolute value distribution. The equations and graph presented target academic and research-oriented audiences, providing insights into the behavior of certain statistical parameters in relation to location metrics. The clear structure and detailed equations ensure the content's usability for educational purposes. #################### File: VW%2010130_EN%281%29.pdf Page: 15 Context: # Relative Dispersion Range Limits of the Type II Absolute Value Distribution For the fitted type II absolute value distribution, the dispersion range limits can then be determined numerically, and their relationships with the relative location are shown in Figure 8. ![Figure 8 - Relative dispersion range limits of the type II absolute value distribution in relationship to the relative location](path/to/image) ## Direct Determination of Statistics For direct determination of the statistics \( z \) and \( \sigma_v \), from the statistics \( \mu \) and \( \sigma \), for \( 1.9131 \leq \frac{\sigma}{\sigma} \leq 6 \), the following approximation can also be used as an inverse function of (2.22) with adequate precision (error related to \( o \) less than 0.02): \[ \xi_{82} \left( \frac{\sigma}{\sigma} \right) \geq 2.1 \left( \frac{\sigma}{\sigma} - 1.9131 \right)^{0.913} + 0.466 \left( \frac{\sigma}{\sigma} - 1.9131 \right)^{1.22} \tag{2.27} \] In addition, the determination of the dispersion range limits for \( 1.9131 \leq \frac{\sigma}{\sigma} \leq 6 \) is carried out directly with the use of the following approximation (error related to \( o \) less than 0.03): \[ \xi_{89.8656} = -1.64 \left( \frac{\sigma}{\sigma} - 1.9131 \right)^{0.62} + 2.075 \left( \frac{\sigma}{\sigma} - 1.9131 \right)^{0.9} + 5.5485 \tag{2.28} \] \[ \xi_{X0.1356} = 2.6 \cdot \exp\left( -\left( \frac{\sigma}{\sigma} - 1.7031 \right)^{0.8} \right) + 1.425 \left( \frac{\sigma}{\sigma} - 1.9131 \right)^{0.9} - 2.1206 \] For \( \frac{\sigma}{\sigma} \geq 6 \), the calculation of the dispersion range limits is carried out according to formula (2.11). --- **Footnotes:** 1. Illustrations, graphics, photographs, and flow charts were adopted from the original German standard, and the numerical notation may therefore differ from the English practice. A comma corresponds to a decimal point, and a period or a blank is used as the thousands separator. Image Analysis: ### Analysis of the Attached Visual Content #### 1. Localization and Attribution: - **Image Number**: Image 1 - **Location on Page**: Center of the page #### 2. Object Detection and Classification: - **Objects Detected**: - **Graph**: Chart displaying a relationship between "Relative location μ/σ" and "Relative scatter range limit". - **Text**: Mathematical equations, descriptive text, footnotes. #### 3. Scene and Activity Analysis: - **Scene Description**: The page contains a graph illustrating relative dispersion range limits for a type II absolute value distribution. Below the graph, there are mathematical equations and explanations regarding the calculations. - **Main Actions**: The graph visualization, mathematical formulations, and explanatory text. #### 4. Text Analysis: - **Detected Text**: - Title: "Figure 8 - Relative dispersion range limits of the type II absolute value distribution in relationship to the relative location" - Various mathematical equations and descriptions detailed below the graph. - Footnotes explaining the notation specifics. - **Content Significance**: - The text provides detailed theoretical explanations and formulas necessary to understand the dispersion range limits for a type II absolute value distribution. The approximations and error precisions are also explained. #### 5. Diagram and Chart Analysis: - **Graph Analysis**: - **Axes**: - X-axis: Labeled as "Relative location μ/σ", ranging from 1.5 to 6.0. - Y-axis: Labeled as "Relative scatter range limit", ranging from 0 to 9. - **Data Trends**: - Two curves are depicted: - \( X_{99.865\%} / σ \) - \( X_{0.135\%} / σ \) - The graph shows increasing trends for both curves as the relative location μ/σ increases. - **Key Insights**: - The relationship between the relative location and the relative scatter range limit is non-linear. - The upper bound \( X_{99.865\%} / σ \) increases at a different rate compared to the lower bound \( X_{0.135\%} / σ \). #### 12. Graph and Trend Analysis: - **Data Points and Trends**: - From 1.5 to 6.0 on the x-axis, the particular scatter range limits increase, suggesting an increasing relationship between the relative location and scatter range limits. - Highlighting the non-linear growth of the variable scatter range limits based on the given equations. #### 13. Graph Numbers: - **Data Points**: - Specific numeric data points aren’t provided in the graph apart from the general trend lines (curves). #### Additional Aspects: - **Ablaufprozesse (Process Flows)**: - The process flow is described for determining the statistics z and σy using given formulas, highlighting sequential steps in the determination and approximation process. - **Prozessbeschreibungen (Process Descriptions)**: - Detailed process descriptions are provided for determining dispersion range limits and the use of approximations for error precision. - **Typen Bezeichnung (Type Designations)**: - The type designation mentioned refers to the "type II absolute value distribution". #### Text Equations: - **Equation (2.27)**: \[ \xi_{2} \left(\frac{\hat{z}}{\hat{\sigma}}\right) \approx 2.1 \left(\frac{\hat{z}}{\hat{\sigma}} - 1.9131\right)^{0.913} + 0.466 \left(\frac{\hat{z}}{\hat{\sigma}} - 1.9131\right)^{1.22} \] - **Equation (2.28)**: \[ \hat{z}_{99.865\%} \approx \frac{\hat{\sigma}}{e} \left(-1.64 \cdot \left(\frac{\hat{z}}{\hat{\sigma}} - 1.9131\right)^{0.62} + 2.075 \cdot \left(\frac{\hat{z}}{\hat{\sigma}} - 1.9131\right)^{0.89} + 5.5485\right) \] \[ \hat{z}_{0.135\%} \approx \frac{\hat{\sigma}}{e} \left[2.6 \cdot \exp \left(\left(\frac{\hat{z}}{\hat{\sigma}} - 1.7031\right) \cdot 0.8\right) + 1.425 \cdot \left(\frac{\hat{z}}{\hat{\sigma}} - 1.9131\right)^{0.9} - 2.1206\right] \] This comprehensive examination encapsulates the intricate details regarding the graph, related calculations, and underlying mathematical explanations present in the visual content. #################### File: VW%2010130_EN%281%29.pdf Page: 16 Context: # 3.2.2 Determination of Capability for Undefined Distribution Models If no fitting distribution model can be assigned to a production characteristic or the measured values from the random samples contradict the assumed distribution model, a distribution-free estimate of the capability indexes is carried out according to the range method, in the following modified form under consideration of the random sample size (see also example 3 in Section 5): ## Capability Indexes for Characteristics with Two-Sided Tolerance Zones \[ \hat{c}_{m} = \frac{G_{o} - \hat{G}_{u}}{\hat{x}_{o} - \hat{x}_{u}} \tag{2.29} \] \[ \hat{c}_{m} = \min \left\{ \frac{G_{o} - \hat{x}_{o,95\%} - \hat{G}_{l}}{\hat{x}_{o} - \hat{x}_{o,95\%} \, \hat{x}_{o,95\%} - \hat{x}_{u}} \right\} \tag{2.30} \] ## Capability Indexes for Characteristics with Upper Limited Tolerance Zone and Natural Limit Zero \[ \hat{c}_{m} = \frac{G_{o}}{\hat{x}_{o} - \hat{x}_{u}} \tag{2.31} \] \[ \hat{c}_{m} = \frac{G_{o} - \hat{x}_{o,95\%}}{\hat{x}_{o} - \hat{x}_{o,95\%}} \tag{2.32} \] ## Capability Indexes for Characteristics with Lower Limited Tolerance Zone Only \[ \hat{c}_{m,k} = \frac{\hat{x}_{o,95\%} - \hat{G}_{l}}{\hat{x}_{o,95\%} - \hat{x}_{u}} \tag{2.33} \] where - \(\hat{x}_{o}\), \(\hat{x}_{u}\): estimated values of the upper and lower dispersion range limits - \(\hat{x}_{o,95\%}\): estimated value of the **50% quantile** In the case of **single values**: \[ \hat{x}_{o,95\%} = \bar{x} \tag{2.34} \] where - \(\bar{x}\): median value, the value that lies in the middle of an ordered sequence of measurements The dispersion range limits are estimated with: \[ \hat{x}_{o} = x_{c} - k \cdot \frac{R}{2} \tag{2.35} \] where - \(x_{c}\): center of the interval - \(k\): constant related to the desired confidence level - \(R\): range of the data Image Analysis: ### Detailed Analysis of the Provided Document: The document appears to be a technical text likely excerpted from a manual or guide. #### 1. Localization and Attribution: - **Image Position**: Single page is displayed. - **Image Number**: Image 1 #### 4. Text Analysis: - **Extracted Text**: - **Page Information**: - "Page 16" - "VW 101 30: 2005-02" - **Section Heading**: - "3.2.2 Determination of capability for undefined distribution models" - **Main Content**: - The text describes statistical methods for determining capability indexes for characteristics with various tolerance zones. - There are several mathematical formulas provided for different scenarios: - Two-sided tolerance zones (Formulas 2.29, 2.30) - Upper limited tolerance zone and natural lower limit zero (Formulas 2.31, 2.32) - Lower limited tolerance zone only (Formula 2.33) - **Variables and Notations**: - \( \tilde{c}_m \), \( \tilde{c}_{mk} \), \( \tilde{x}_M \), \( \tilde{x}_u \), \( \tilde{x}_{50\%}\), \( \tilde{x} \) - \( G_o, G_u, k, R \) - **Additional Notes**: - Definition of single values and median value. - Final formulas provide estimations for dispersion range limits (Formula 2.35). - **Contextual Significance**: - The extracted formulas and methodologies are essential for determining statistical capabilities without predefined distribution models, which is critical in quality control and manufacturing processes. #### 5. Diagram and Chart Analysis: - **Absence of Diagrams or Charts**: - The page contains purely textual and mathematical content with no diagrams or charts to analyze. #### 10. Contextual Significance: - **Contribution to Overall Document**: - This text is likely part of a larger technical manual or guide that provides methodologies for determining statistical capability. It focuses on cases where typical distribution models do not apply, indicating an advanced level of statistical quality control. #### Ablufprozesse (Process Flows) / Prozessbeschreibungen (Process Descriptions): - **None Depicted**: - There are no process flows or detailed process descriptions within the content of this page. #### Typen Bezeichnung (Type Designations): - **Identification**: - This section is part of a larger document ("VW 101 30: 2005-02") and specifically deals with undefined distribution models in statistical analysis. ### Summary: This page provides detailed methodological instructions for calculating capability indexes for manufacturing characteristics without predefined distribution models. It includes specific formulas and conditions for their application, making it a critical reference for professionals in quality control and manufacturing processes. #################### File: VW%2010130_EN%281%29.pdf Page: 17 Context: ```markdown x_c = \frac{x_{\text{max}} + x_{\text{min}}}{2} (2.36) R = x_{\text{max}} - x_{\text{min}} : \text{ range} (2.37) x_{\text{max}}, x_{\text{min}} : \text{ maximum and minimum measured value, respectively, of the effective total random sample} By the correction factor k = \frac{6}{d_n} (2.38) the effective random sample size n_e is taken into consideration, where d_n : \text{ expected value of the } w \text{ distribution } ^{5} The value d_n is given in Table 1 for a few random sample sizes n_e. | n_e | d_n | |-----|------| | 20 | 3.74 | | 25 | 3.93 | | 30 | 4.09 | | 35 | 4.21 | | 40 | 4.32 | | 45 | 4.42 | | 50 | 4.50 | For random sample sizes that are greater than 20, the expected values of the w distribution can be determined according to the following approximation formula: d_n \equiv 1.748 \cdot \ln(n_e)^{6.63} (2.39) In the case of a frequency distribution of classified measured values \hat{x}_0, \hat{x}_d \text{ are the upper limit, lower limit, respectively, for the top/bottom occupied class} and \hat{x}_{90\%} = \hat{x}_k + \frac{n/2 - A_k}{a_k} \cdot \Delta x \text{ for } A_k < \frac{n}{2} \leq A_k + a_k (2.40) where x_k : \text{ lower limit of the } k^{th} \text{ class} \Delta x : \text{ class width} a_k : \text{ absolute frequency of the measured values in the } k^{th} \text{ class} A_k : \text{ absolute cumulative frequency of the measured values to the lower limit of the } k^{th} \text{ class} ``` Image Analysis: ### Analysis of the Visual Content #### 1. Localization and Attribution: - **Image Identification:** - Single image on the page identified as **Image 1**. #### 4. Text Analysis: - **Text Detected:** - Page details: "Page 17, VW 101 30: 2005-02". - Mathematical notations and formulae. - Table titled "Expected value of the w distribution in relationship to nₑ". - Linguistic content explaining how to interpret the values in the table. - **Mathematical Formulae and Content:** - Several mathematical expressions are presented: - \( x_c = \frac{x_{\max} + x_{\min}}{2} \) - \( R = x_{\max} - x_{\min} \) - \( \frac{6}{d_n} \) - Description explaining the different symbols: - \( x_{\max}, x_{\min} \): Maximum and minimum measured values. - \( R \): Range. - \( k = \frac{6}{d_n} \): A correction factor involving expected value of the \( w \) distribution \((d_n)\). #### 5. Diagram and Chart Analysis: - **Table Content Analysis:** - Title: "Expected value of the w distribution in relationship to nₑ". - Columns: - \( nₑ \): Represents the effective random sample size. - \( d_n \): Represents the expected value of the \( w \) distribution. - Data presented in the table: - \( nₑ = 20, d_n = 3.74 \) - \( nₑ = 25, d_n = 3.93 \) - \( nₑ = 30, d_n = 4.09 \) - \( nₑ = 35, d_n = 4.21 \) - \( nₑ = 40, d_n = 4.32 \) - \( nₑ = 45, d_n = 4.42 \) - \( nₑ = 50, d_n = 4.50 \) #### 12. Graph and Trend Analysis: - **Formulae and Trends:** - For \( nₑ > 20 \), the expected value of the \( w \) distribution is calculated with the formula: - \( d_n \approx 1.748 - (\ln(n_e))^{0.602} \) - Additional formula for frequency distribution of classified measured values: - Upper limit and lower limit represented as \( x_{0}, x_{u} \), respectively. - The formula for the highest value in frequency distribution involves additional parameters including class width, frequency, and cumulative frequency. #### 13. Graph Numbers: - **Numerical Data points:** - For \( nₑ \): - 20 - 25 - 30 - 35 - 40 - 45 - 50 - For \( d_n \): - 3.74 - 3.93 - 4.09 - 4.21 - 4.32 - 4.42 - 4.50 ### Summary: - **Content Overview:** - The page seems to discuss statistical measures for sample sizes. - Provides mathematical formulas and a table to understand the expected value of a specific w distribution. - Detailed descriptions and formulae help in calculating these values for different sample sizes. - **Significance:** - The information is crucial for statistical analysis and understanding distribution expectations for various sample sizes. - Helps in making informed decisions based on statistical data. #################### File: VW%2010130_EN%281%29.pdf Page: 18 Context: # 3.3 Limit values of machine capability To obtain the machine capability for a considered characteristic, the capability indexes determined must fulfill the following requirement with respect to the specified limit values \( C_{mk, \text{green}} \) and \( C_{mk, \text{red}} \): ## Characteristics with two-sided tolerance zones: \[ \hat{C}_{mk} \geq C_{mk, \text{limit}} \tag{3.1} \] ## Characteristics with one-sided tolerance zone only6: \[ \hat{C}_{mk} \geq C_{k, \text{limit}} \tag{3.2} \] with an effective random sample size of \( n_e \geq 50 \) Unless otherwise agreed, the following capability limit values apply: \[ C_{k, \text{limit}} = 2.0 \] \[ C_{mk, \text{limit}} = 1.67 \] In cases where, with reasonable effort, an examination can only be carried out with an effective random sample size less than 50, the resulting uncertainty of the capability indexes determined must be taken into consideration by applying correspondingly higher limit values as follows. The determination of limit values for effective random sample sizes smaller than 50 is related here to limit values that comply with the requirement from (3.1) or (3.2) for the population to be investigated with 95% probability (lower confidence range limits). With the assumption of a normally distributed population, these result from the upper confidence range limit of the standard deviation: \[ \sigma_e = \hat{\sigma} \cdot \frac{49}{\sqrt{2 \cdot n_e}} \tag{3.3} \] and the statistical percentage range for the production dispersion: \[ X_{99.865\%} = X_{0.135\%} \pm \hat{z}_{99.865\%} \left( \frac{1 + \frac{1}{2 \cdot 50}}{\sqrt{49}} \right) \tag{3.4} \] where - \( z_{99.865\%} = 3.0 \): quantile of the standardized normal distribution - \( \chi^{2}_{49\%} = 33.9 \): quantile of the chi-square distribution with a degree of freedom of \( f = 49 \) (see also [1]) 6 Although no limit value for \( C_m \) is specified for characteristics with upper limited tolerance zone only, a \( C_m \) value is to be determined and specified, since from the comparison of this value to the \( C_m \) value, it is possible to recognize whether an undesirable situation shift exists. For example, if the \( C_{mk} \) value is higher than the \( C_{m} \) value, the distribution lies closer to the natural limit value zero than to the upper limiting value. Image Analysis: Here is a comprehensive analysis of the visual content provided, addressing the relevant aspects: ### Localization and Attribution - **Image Position:** This image appears to be a single page, numbered as **Image 1** based on its position. ### Text Analysis **Extracted Text:** - **Main Title:** "Limit values of machine capability" - **Section:** "3.3 Limit values of machine capability" - **Content:** - Requirements for machine capability indexes. - Formulas and conditions with respect to specified limit values. - Commentary on the effectiveness and sample sizes. - Confidence range limits and statistical percentage range for production dispersion. - Definitions and essential concepts like quantiles and degrees of freedom. **Analysis:** - **Formulas and Conditions:** The text includes mathematical formulas (e.g., \( \hat{c}_{m} \geq c_{m,\text{limit}} \)) to determine machine capability, addressing one and two-sided tolerance zones. - **Context:** Used in engineering or quality assurance for defining machine capability limits. - **Significance:** Ensures machinery operates within specified parameters, which is crucial for maintaining product quality and operational efficiency. ### Diagram and Chart Analysis **Mathematical Expressions and Data:** - **Formulas:** - Two-sided tolerance zones: \( \hat{c}_{m} \geq c_{m,\text{limit}} \) and \( \hat{c}_{mk} \geq c_{mk,\text{limit}} \) - One-sided tolerance zone: \( \hat{c}_{mk} \geq c_{mk,\text{limit}} \) - Effective random sample size: \( n_{B} \geq 50 \) - Standard deviation upper confidence range limit: \( \sigma_{o} = \sigma \cdot \sqrt{\frac{49}{\chi^2_{5\%/49}}} \) - Statistical percentage range: \( x_{99.865\%} = \bar{x} \pm t_{99.865\%} \cdot \left( 1 + \frac{1}{2 \cdot 50} \right) \cdot \sqrt{\frac{49}{\chi^2_{5\%/49}}} \cdot \sigma \) - **Values:** - Capability limit values: \( c_{n,\text{limit}} = 2.0 \) and \( c_{nk,\text{limit}} = 1.67 \) - Quantiles: \( t_{99.865\%} = 3.0 \) - Chi-square distribution: \( \chi^2_{5\%/49} = 33.9 \) ### Process Descriptions **Requisite Conditions:** - Machine capability indexes must fulfill specified limit values and be examined with effective random samples for accuracy. - Adjustments for sample sizes smaller than 50 are provided, ensuring the results maintain statistical validity. ### Contextual Significance **Overall Document Context:** - This page is from a technical document or standard, likely related to engineering, production quality control, or machinery maintenance. - **Page Number:** "Page 18" - **Document Title:** "VW 101 30: 2005-02" signifies the document originates from a specific set of standards or guidelines relevant to the Volkswagen group or a similar entity. ### Metadata Analysis **Implied Information:** - **Date:** February 2005 (as part of the document title). - **Context:** Standards or guidelines relevant to a specific period, highlighting how machine capability limits were defined and analyzed during that time. ### Anomaly Detection - **Noticeable Elements:** None detected that deviate from the technical and formulaic structure of the document. ### Perspective and Composition **Image Perspective:** - The image is scanned or captured from a directly overhead perspective, ensuring the text is legible and formatted correctly for analysis. ### Conclusion The page provides detailed guidelines on determining and validating machine capability through statistical measures, ensuring machinery adheres to specific performance standards. The content, heavy with formulas and statistical values, underscores its technical and formal nature, playing a critical role in quality assurance and operational efficiency within a production setting. #################### File: VW%2010130_EN%281%29.pdf Page: 19 Context: By transformation and substitution in the evaluation formulas (2.1) and (2.2), this results in the **capability limit values for the population** \[ c_r \geq c_{r,\text{limit}} \cdot \sqrt{\frac{X_{r,\text{max}}}{49}} = 0.832 \cdot c_{\text{limit}} \tag{3.5} \] \[ c_{mk} \geq c_{k,\text{limit}} \cdot \frac{1}{1 + \sqrt{100}} \cdot \sqrt{\frac{X_{k,\text{max}}}{49}} = 0.824 \cdot c_{k,\text{limit}} \tag{3.6} \] For effective random sample sizes \( n_e < 50 \), this results in the following **fitted capability limit values**: \[ \hat{c}_r \geq c_{r,\text{limit}} \cdot 0.832 \cdot \sqrt{\frac{f}{X_{r,k}}} \tag{3.7} \] \[ \hat{c}_{mk} \geq c_{k,\text{limit}} \cdot 0.824 \cdot \left(1 + \frac{1}{2 n_e}\right) \cdot \sqrt{\frac{f}{X_{k,m}}} \tag{3.8} \] with the degree of freedom \[ f = n_e - 1 \tag{3.9} \] **Example:** For specified capability limit values of \( c_{r,\text{limit}} = 2.0 \), \( c_{k,\text{limit}} = 1.67 \) and an effective random sample size of \( n_e = 20 \), according to the formulas (3.7) to (3.9) the following fitted limit values result for characteristics with two-sided tolerance zones: \[ \hat{c}_r \geq 2.0 \cdot 0.832 \cdot \sqrt{\frac{20 - 1}{10.1}} = 2.28 \] \[ \hat{c}_{mk} \geq 1.67 \cdot 0.824 \cdot \left(1 + \frac{1}{2 \cdot 20}\right) \cdot \sqrt{\frac{20 - 1}{10.1}} = 1.93 \] --- 7. The determination of the adapted capability limit values using formulas (4.7) to (4.9) is also used for populations without normal distribution, since there are no other methods for these at this time and thus at least a usable consideration of a random sample size that is less than 50 is carried out. Image Analysis: ### Analysis of the Attached Visual Content #### Localization and Attribution: - **Single Image**: - The document contains only one image. - **Image Number**: Image 1 #### Text Analysis (Image 1): - **Extracted Text**: The content includes well-structured mathematical formulas and a textual description explaining capability limit values for the population and effective random sample sizes. **Text Content**: - **Page Header**: - Page 19 - VW 101 30:2005-02 - **Main Text**: ``` By transformation and substitution in the evaluation formulas (2.1) and (2.2), this results in the capability limit values for the population. Equation 3.5: c_{m)>=c{mk,limit}\sqrt{\frac{K_{l,\delta}{2}}{49}} =0,832 * c_{mk,limit} Equation 3.6: c_{mk}>c_{mk,\limt}\frac(1)(1+\frac{1}{100}) * \sqrt{\frac{K^2_{l,delta}}{49}} = 0,824 * c_{mk,limit} For effective random sample sizes n-.... <50, the results in the following fitted capability limit values Equation 3.6: ĉ_{m)>=c{mk,limit} 0,832 * \sqrt{\frac(f}{K^2_{l, delta}} Equation 3.7: ĉ_{mk}>{cap,limit} \cdot 0,.824 * \sqrt{\frac{l+\frac{1}{2}\cdot l){*f}{K_{l,delta}}l{\sqrt{f}{n-1}} .... As relative random size for n = <... \cdot Example: For specific cap limit value of c_{cm,limit}=2,0 c_{m\=limit = 1,67} and effective random joint sample size of \cdot n_{e} = 2.... according to form... Equation 4.9-.....Given the following fitted .... C_{m}=2',03 * C) .....[complex formulay] \sqrt(20-1)(cm200)= (m=1,67c incurred indicated \sqrt{\frac(f}{K^2_{4...osure followable '' **Footnote**: The determination of the adapded capability limit values using formula f={ 1 to 0.1th is also used for populations without normal attributes #### Scene and Activity Analysis (Image 1): - **Scene Description**: The entire image is a page from a technical or academic text. It primarily features complex mathematical content related to capability limit evaluation formulas. - **Activities**: The primary activities involve mathematical transformations, substitutions, and evaluations of capability limit values. #### Color Analysis (Image 1): - **Dominant Colors**: Predominantly black text on a white background. - **Impact on Perception**: The contrast between black text and white background makes the text highly readable and professional, suitable for academic and technical documentation. #### Perspective and Composition (Image 1): - **Perspective**: The image is a scanned or photographed page from a document, seen from a top-down or direct perspective. - **Composition**: The layout is similar to a standard academic page, with header, main content, numbered formulas, and a footnote. - **Elements Arrangement**: Clear hierarchical structuring of formulas and supporting text for easy understanding and reference. #### Contextual Significance (Image 1): - **Document Context**: Given the technical and formulaic content, it is likely part of a larger document on statistical analysis or quality control. - **Contribution to Message**: The page contributes to explaining the methodology for calculating capability limits within a given statistical context. ### Conclusion: The image analyzed is a page from a technical document related to statistical evaluation formulas for capability limits. It involves detailed mathematical expressions aimed at professionals or academics in fields such as quality control, statistics, or engineering. The text is well-organized, with clear structuring and notation to facilitate understanding of the complex formulas presented. The page is designed to be informative and easily readable, using a simple black-and-white color scheme. #################### File: VW%2010130_EN%281%29.pdf Page: 20 Context: # 3.4 Statistical Tests Generally, the measurements of a machine capability investigation shall not exhibit any: - unexpectedly great deviation of single measured values (outliers) in comparison to the dispersion of other measured values, - significant change of the production location during the sampling, and - significant deviation from the expected distribution model. Otherwise, additional systematic influences on production have to be taken into consideration. The causes should then be known for this behavior and their effect should be acceptable in order to fulfill the requirement of a secure manufacturing process. Therefore, to test the above mentioned criteria, the appropriate statistical tests shall be used during a machine capability investigation. Since these tests are described in detail in standards and standard statistics references, they will only be indicated by the following references: The following tests are to be carried out in the scope of a machine capability investigation: - **Test for outliers** using the distribution-free test according to Hampel in modified form (see VDA 4 standard VW 10133) - **Test for change of the production location** using the distribution-free Run-Test according to Swed-Eisenhart (see [1]) - **Test for deviation from the normal distribution** according to Epps-Pulley (see ISO 5479) - **Test for deviation from any specified distribution model** using the chi-square test (see [1]) The statistical tests all proceed according to the following system: 1. Setting up the **null hypothesis** \(H_0\) and the **alternative hypothesis** \(H_a\), e.g., - \(H_0\): The population of the measured values of the characteristic considered has normal distribution - \(H_a\): The population of the measured values of the characteristic considered does not have normal distribution 2. Specification of the **confidence level** \(\alpha = 1 - \alpha\) or **probability of error** \( \alpha\) 3. Setting up the formula for the **test variable** 4. Calculating the **test value** from the random sample values according to the test variable formula 5. Determining the **threshold value** of the test distribution 6. Comparison of the test value to the threshold value for decision of whether a contradiction to the null hypothesis exists and thus the alternative hypothesis is valid. It should be noted that in a statistical test with the specified confidence level \( \alpha \), contradiction to the null hypothesis can be proven, e.g., that a significant deviation of the measured values from a normally distributed population exists. If no contradiction to the null hypothesis results from the test result, this is not a confirmation of the validity of the null hypothesis. In this case, it cannot be proven that the defined confidence level that a normally distributed population exists, for example. Then, analogously to the legal principle "if in doubt, find for the defendant," a decision is simply made for assumption of the null hypothesis. The probability of error \( \alpha \) indicates the risk of rejecting the null hypothesis on the basis of the test result, although it applies (as risk). However, not just any small value can be specified for the probability of error, since that would increase, e.g., the risk of not discovering an actual deviation from a normal distribution (as risk). Image Analysis: ## Analysis of Image 1 ### 1. Localization and Attribution: - **Image Identifier**: Image 1 - **Location**: The image appears to be a standalone page from a document. ### 4. Text Analysis: - **Extracted Text**: ``` Page 20 VW 101 30: 2005-02 3.4 Statistical tests Generally, the measurements of a machine capability investigation shall not exhibit any – unexpectedly great deviation of single measured values (outliers) in comparison to the dispersion of other measured values, – significant change of the production location during the sampling and – significant deviation from the expected distribution model. Otherwise additional systematic influences on production have to be taken into consideration. The causes should then be known for this behavior and their effect should be acceptable in order to fulfill the requirement of a secure manufacturing process. Therefore, to test the above mentioned criteria the appropriate statistical tests shall be used during a machine capability investigation. Since these tests are described in detail in standards and standard statistics references, they will only be indicated by the following references: The following tests are to be carried out in the scope of a machine capability investigation: – Test for outliers using the distribution-free test according to Hampel in modified form (see Volkswagen standard VW 10133) – Test for change of the production location using the distribution-free Run-Test according to Swed-Eisenhard (see [1]) – Test for deviation from the normal distribution according to Epps-Polley (see ISO 5479 – Test for deviation from any specified distribution model using the chi-square test (see [1]) The statistical tests all proceed according to the following system: – Setting up the null hypothesis H0 and the alternative hypothesis H1, e.g. H0: The population of the measured values of the characteristic considered has normal distribution H1: The population of the measured values of the characteristic considered does not have normal distribution – Specification of the confidence level γ = 1-α or probability of error α – Setting up the formula for the test variable – Calculating the test value from the random sample values according to the test variable formula – Determining the threshold value of the test distribution – Comparison of the test value to the threshold value for decision of whether a contradiction to the null hypothesis exists and thus the alternative hypothesis is valid It should be noted that in a statistical test with the specified confidence level γ possibly only a contradiction to the null hypothesis can be proven, e.g. that a significant deviation of the measured values from a normally distributed population exists. If no contradiction to the null hypothesis results from the test result, this is not a confirmation of the validity of the null hypothesis. In this case, it cannot be proven within the defined confidence level that a normally distributed population exists, for example. Then, analogously to the legal principle “if in doubt, find for the defendant,” a decision is simply made for assumption of the null hypothesis. The probability of error α indicates the risk of rejecting the null hypothesis on the basis of the test result, although it applies (α risk). However, not just any small value can be specified for the probability of error, since that would increase, e.g., the risk of not discovering an actual deviation from a normal distribution (β risk). ``` - **Content Analysis**: - **Title and Section**: "3.4 Statistical tests" is the section title, indicating the focus is on statistical testing within machine capability investigations. - **Key Points**: - Discusses statistical tests to ensure consistency and lack of deviation in machine capability measurements. - Specifies conditions and systematic influences that must be considered. - Tests mentioned: - Outliers (Hampel test) - Change in production location (Run-Test) - Normal distribution deviation (Epps-Polley test) - Chi-square test for specified distribution model. - Describes setting up hypotheses (null and alternative), confidence levels, test variable formulas, calculating test values, threshold values, and decision making. ### 12. Diagram and Chart Analysis: - There are no diagrams or charts in the image. ### 13. Graph Numbers: - Since no graphs are present, numerical data points analysis isn't applicable. ### 15. Tables: - There are no tables in the image. ### 8. Color Analysis: - **Color Composition**: - Dominantly black text on a white background, providing high contrast and readability. ### 9. Perspective and Composition: - **Perspective**: - Front-facing view of a text document. - **Composition**: - The document is well-structured with clear headings, subheadings, and bullet points for clarity and ease of reading. ### 10. Contextual Significance: - **Context and Contribution**: - Likely part of a larger technical manual or guidelines document related to machine capability and statistical analysis. - Contributes valuable information on how to conduct and interpret statistical tests in manufacturing processes. ## Summary: Image 1 is a clearly structured and detailed section from a technical manual focused on statistical tests relevant to machine capability investigations. It outlines key tests, procedural steps for hypothesis testing, and considerations for secure manufacturing processes. The content is technical and highly relevant for professionals involved in machine capability and quality assurance. #################### File: VW%2010130_EN%281%29.pdf Page: 21 Context: # 4 Carrying out a machine capability investigation A machine capability investigation (MFI) is carried out according to the sequence shown in Figures 9 to 11. ## Flowchart of Machine Capability Investigation 1. Start 2. **4.1 Test equipment use** 3. **4.2 Sampling** - Conditions for MFI fulfilled? - **Yes** → **4.4 Data analysis** - **No** → **4.3 Special regulation for restricted MFI** 4. **4.5 Documentation** 5. **4.6 Results evaluation** - Evaluation repeat? - **Yes** → Back to **4.5 Documentation** - **No** → Is the machine capable? - **Yes** → **4.7 Machine optimization** - **No** → Feasible machine optimization? - **Yes** → **4.8 Handling of incapable machines** - **No** → End --- **Figure 9 - Sequence of a machine capability investigation** Image Analysis: ### Image Analysis **Image Number: Image 1** #### Object Detection and Classification - **Objects Detected:** - Text content - Flowchart elements including shapes like ovals, rectangles, and diamonds. - Arrows indicating process flow. - **Key Features of Detected Objects:** - The flowchart begins with a start point indicated by an oval shape. - It includes various process steps, decisions, and conditions. - Arrows show the direction of the process flow from one step to another. #### Scene and Activity Analysis - **Entire Scene Description:** - The image is a flowchart illustrating the sequence of a machine capability investigation. - It is divided into different steps starting from "Test equipment use" and including steps like "Sampling," "Data analysis," and "Results evaluation." - **Activities Taking Place:** - The flowchart delineates various activities carried out during a machine capability investigation. - Decision points lead to different actions based on the results of each step. #### Text Analysis - **Text Content:** - "Page 21 VW 101 30: 2005-02" - "4 Carrying out a machine capability investigation" - "Start" - "4.1 Test equipment use" - "4.2 Sampling" - "Conditions for MFI fulfilled" - "No" - "4.3 Special regulation for restricted MFI" - "Yes" - "4.4 Data analysis" - "4.5 Documentation" - "4.6 Results evaluation" - "Evaluation repeat" - "Machine capable" - "No" - "Feasible machine optimization" - "Yes" - "No" - "4.7 Machine optimization" - "4.8 Handling of incapable machines" - "Yes" - "End" - "Figure 9 - Sequence of a machine capability investigation" - **Content Significance:** - The text describes different stages in a machine capability investigation process. - It provides specific instructions and decision points for undertaking various actions depending on the results at each stage. #### Diagram and Chart Analysis - **Axes, Scales, and Legends:** - Not applicable. This is a flowchart without any axes, scales, or legends. - **Key Insights:** - The flowchart offers a structured methodology for conducting a machine capability investigation. - It identifies critical decision points that determine the subsequent steps, facilitating systematic evaluation and optimization of machine capability. #### Ablaufprozesse (Process Flows) - **Process Flow Description:** - The flowchart starts with equipment testing, proceeds through sampling, and assesses whether MFI (Machine Functional Index) conditions are met. - If conditions are not met, it refers to special regulations. - Further steps involve data analysis and documentation, results evaluation, and machine optimization. - Final steps determine whether the machine is capable or if further actions like handling incapable machines are necessary. #### Prozessbeschreibungen (Process Descriptions) - **Detailed Process Description:** - The process begins with testing the equipment (4.1). - Followed by sampling (4.2). - A decision is made whether conditions for MFI are fulfilled. - Based on conditions, different steps such as data analysis (4.4), documentation (4.5), and results evaluation (4.6) are followed. - Machine optimization (4.7) or handling of incapable machines (4.8) concludes the process. #### Trend and Interpretation - **Trends Identified:** - The process emphasizes systematic data collection, analysis, and decision-making. - A focus is placed on optimization and proper handling of incapable machines based on evaluation results. #### Perspective and Composition - **Image Perspective:** - The image is taken from a straightforward, eye-level perspective, providing clear visibility of all flowchart elements in a top-down manner. - **Image Composition:** - The elements are arranged sequentially, with arrows guiding the viewer through the process from start to finish. - Decision points and action steps are clearly delineated to ensure a logical flow of information. ### Summary The image provides a comprehensive flowchart outlining the sequence of conducting a machine capability investigation. Through a series of steps involving testing, sampling, analysis, and decision-making, the chart presents a systematic approach to achieving machine optimization or handling incapable machines. #################### File: VW%2010130_EN%281%29.pdf Page: 22 Context: # 4.4 Data Analysis ## 4.4.1 Selection of the Expected Distribution Model ## 4.4.2 Test for Outliers - **Outliers present?** - Yes: - **4.4.3** Take outliers out of the calculation of statistics - No: - **4.4.4** Test for change of the production location - **4.4.5** Test for deviation from the specified distribution model ## 4.4.4 Test for Change of the Production Location ## 4.4.5 Test for Deviation from the Specified Distribution Model - **Deviation from distribution model?** - Yes: - **Distribution-free evaluation** - No: - **Normal distribution?** - Yes: - **4.4.6** Evaluation according to normal distribution - No: - **4.4.7** Evaluation according to specified model ## Continued at 4 --- **Figure 10 - Sequence of Data Analysis** Image Analysis: ### Analysis of the Attached Visual Content **1. Localization and Attribution:** - **Identification and Location:** There is a single image on the page containing a flowchart. - **Numbering:** Image 1. **2. Object Detection and Classification:** - **Objects Identified:** - Flowchart components including flowchart shapes such as ovals, rectangles, diamonds, and arrows. - **Key Features:** - The flowchart outlines a process with decision points and actions. **4. Text Analysis:** - **Detected Text:** - Page 22 - VW 101 30: 2005-02 - 4.4 Data analysis - 4.4.1 Selection of the expected distribution model - 4.4.2 Test for outliers - Outliers present - 4.4.3 Take outliers out of the calculation of statistics - no - 4.4.4 Test for change of the production location - 4.4.5 Test for deviation from the specified distribution model - Deviation from distribution model - yes - 4.4.6 Evaluation according to normal distribution - 4.4.7 Evaluation according to specified model - no - normal distribution - Continued at 4 - Distribution-free evaluation - Figure 10 - Sequence of data analysis - **Content Analysis:** - The text describes the steps and decision points involved in the process of data analysis. It begins with selecting an expected distribution model and tests for outliers, followed by actions based on whether outliers are present. The flowchart includes various decision paths based on the results, including the possible need for a change in the production location, evaluation according to a normal distribution, or a distribution-free evaluation. The text conveys a systematic approach to analyzing data and handling deviations. **5. Diagram and Chart Analysis:** - **Data and Trends Identified:** - The diagram is a process flowchart depicting the sequence of steps and decision points in data analysis. - **Axes, Scales, and Legends:** - Not applicable. - **Key Insights:** - The flowchart provides a structured methodology for data analysis, highlighting critical points where decisions are to be made regarding the statistical treatment of data. **8. Color Analysis:** - **Color Composition:** - The image is primarily in black and white, using text and shapes to convey the flow of the process. - Dominant Colors: Black text and lines on a white background. **9. Perspective and Composition:** - **Perspective:** - The image is presented from a standard, straight-on view typical for diagrams and charts. - **Composition:** - The flowchart is vertically aligned, with each step or decision point connected by arrows to indicate the flow of the process. **12. Graph and Trend Analysis:** - **Trends and Interpretation:** - The flowchart indicates a flow from generalized data analysis to specific actions based on statistical testing outcomes. Every potential path has been delineated with steps designed to handle variations in data distributions and outlier management. - **Detailed Breakdown:** - The flowchart starts with a broad step of "4.4 Data analysis," which then branches into: - Selection of the expected distribution model - A test for outliers - If outliers are present, they are taken out of the calculation - Tests for change of production location and deviations from the expected distribution model - If deviations are present, evaluation processes are outlined based on normal distribution or specified model. By analyzing this diagram, users can follow a structured approach to data analysis, considering outliers, production changes, and deviations in distribution models to ensure accurate evaluation. #################### File: VW%2010130_EN%281%29.pdf Page: 23 Context: # 4.6 Results Evaluation ```mermaid flowchart TD A[Outliers present?] -->|yes| B[Outliers due to incorrect measurements?] A -->|no| C[Change of production location?] B -->|yes| D[Evaluation repeat
Continued at 4] B -->|no| E[Cause known and effect acceptable?] C -->|yes| F[Deviation from distribution model?] C -->|no| E F -->|yes| G[Other distribution model possible?] F -->|no| E G -->|yes| D G -->|no| E E -->|yes| H[Capability indexes less than limit values?] E -->|no| I[Machine incapable
Continued at 4] H -->|yes| J[Machine capable
Continued at 4] H -->|no| I ``` **Figure 11 - Sequence of the results evaluation** Image Analysis: ### Image Analysis #### 1. Localization and Attribution - **Image Position**: Only one image is present on the page. - **Image Number**: Image 1 #### 3. Scene and Activity Analysis - **Scene Description**: The image is a flowchart depicting the process flow for the sequence of results evaluation. - **Activity Description**: It shows the decision-making steps in evaluating results, starting from checking for outliers, changes in production location, deviations from distribution models, and evaluating machine capability. #### 4. Text Analysis - **Detected Text**: - "4.6 Results evaluation" - "Outliers present" - "Outliers due to incorrect measurements" - "Change of production location" - "Deviation from distribution model" - "Other distribution model possible" - "Evaluation repeat Continued at 4" - "Cause known and effect acceptable" - "Capability indexes less than limit values" - "Machine capable Continued at 4" - "Machine incapable Continued at 4" - "Figure 11 - Sequence of the results evaluation" - "Page 23" - "VW 101 30: 2005-02" - **Text Analysis**: This text defines the steps and decisions needed to evaluate results systematically. #### 6. Product Analysis - **Product Description**: Not applicable as the image does not depict a product but a flowchart. #### 7. Anomaly Detection - **Anomalies**: No noticeable anomalies. The flowchart appears to be standard and designed correctly without any unusual or unexpected elements. #### 8. Color Analysis - **Color Composition**: The flowchart is in black and white. - **Dominant Colors**: Black and white. - **Impact on Perception**: The use of black and white is conventional for technical diagrams, ensuring clarity and readability. #### 9. Perspective and Composition - **Perspective**: The image is viewed from a straight, eye-level perspective typical for diagrams. - **Composition**: The elements are arranged logically from the top to the bottom, with decision points leading to different paths, indicating a structured process flow. #### 10. Contextual Significance - **Context Analysis**: This image likely belongs to a technical or procedural document related to evaluating machine capabilities or production processes. - **Contribution to Overall Message**: The flowchart helps the reader or user understand the sequence and decision points involved in result evaluation, contributing to a methodical approach. #### 12. Graph and Trend Analysis - **Graph Description**: The flowchart represents decision branches and corresponding actions based on specific evaluation criteria. - **Trend Interpretation**: The flow suggests a structured approach to handling deviations and ensuring machine capabilities are within acceptable limits. #### Additional Aspects #### Ablaufprozesse (Process Flows) - **Process Flow Description**: - **Step 1**: Check for outliers. - **Step 2**: If outliers are present, determine if due to incorrect measurements. - **Step 3**: If no incorrect measurements, check for change in production location. - **Step 4**: If no change in production location, check for deviation from distribution model. - **Step 5**: If deviation exists, evaluate if other distribution models are possible. - **Step 6**: Repeat evaluation if needed. - **Step 7**: If cause of deviation is known and acceptable, and capability indexes are within limits, the machine is capable. If not, the machine is deemed incapable. #### Prozessbeschreibungen (Process Descriptions) - **Process Description**: The process involves several decision points at which specific actions are taken based on the data evaluation, ensuring a systematic and comprehensive approach to result evaluation. #### Typen Bezeichnung (Type Designations) - **Type Designations**: Not explicitly mentioned but implied types include result status (outliers, correct measurements), process elements (distribution models, capability indexes), and outcomes (machine capable/incapable). #### Tables - **Table Analysis**: Not applicable as no tables are included in the image. This comprehensive examination identifies the logical flow and decision points crucial for evaluating results in a systematic manner. #################### File: VW%2010130_EN%281%29.pdf Page: 24 Context: # 4.1 Test Equipment Use Test equipment shall only be used for the MFI that has been released by the responsible department for the planned test process. ## 4.2 Sampling An MFI relates to only one production characteristic or one machine parameter. Generally, the single measurements of the random samples are recorded for evaluation. In the case of minimally recorded measurements in a class subdivision of the value range (tally), the frequency distribution of the classified measurements can also be recorded instead. So, essentially only the machine influence is recorded in an MFI, the following conditions shall be complied with in the production of random sample parts: - A uniform blank batch and a uniform preparation (supplier, material) shall be ensured during the investigation. During the MFI, the machine or system shall always be operated by the same operator. - The premanaging quality of the characteristics to be evaluated must correspond to the required production specifications. - The number of parts to be produced (random sample size) should generally be 50. If this random sample size is difficult to obtain for economic or technical reasons, a smaller one is also permissible. Then the corresponding higher limit values according to Table 3 or the formulas (3.7) and (3.8) have to be complied with. However, the random sample size (i.e. without outliers) must be at least 20. - The parts shall be produced immediately after each other and numbered according to the manufacturing sequence. All specified characteristics shall be tested on each part. - The MFI shall only be carried out with the machine at operating temperature. "Operating temperature" is to be defined for each use case. - The test parts are to be produced under the standard production conditions required for the machine (i.e. with the cycle time and the machine adjustment parameters as in standard production). - Depending on the project, special specifications shall be set so that at the beginning of the MFI, it is ensured that, e.g., the tooling is broken in and that the end of the tooling lifetime does not lie within the MFI. - Tooling change, manual tooling adjustments or other changes of machine parameters shall not be carried out during the MFI. Automatic tooling corrections due to integrated measuring controls are excepted from this. - If there are machine malfunctions during the MFI that influence the characteristic to be investigated, the MFI must be started over again. - The measuring method must be specified before the investigation and agreed upon between supplier and customer. During the production of different parts (different part numbers, e.g., steel shaft / cast iron shaft) on one machine that can additionally have different characteristics, MFIs are to be carried out for all these parts. Image Analysis: ## Comprehensive Examination of the Attached Visual Content ### 1. Localization and Attribution: - The document comprises a single page containing textual content divided into sections with headings and paragraphs. ### 2. Text Analysis: - The document contains text in English and is structured into sections. - **Heading:** "4.1 Test equipment use" and "4.2 Sampling" - **Subsections:** Bulleted and numbered lists describing processes and conditions. - **Footnote:** A small section at the bottom of the page with additional information. #### Detailed Breakdown of Text Content: - **Section 4.1: Test equipment use** - **Content:** - The test equipment is specified for use only with the MFI (Machine Function Investigation) that has been approved by the responsible department for the planned test process. - **Section 4.2: Sampling** - **Content:** - AMFI relates to only one production characteristic or machine parameter. Measurements of random samples are recorded. - Specific conditions for the production of random sample parts are detailed. - Uniform blank batch and preparation must be ensured. - The premachining quality must meet production specifications. - Number of parts, random sample size should be 50 (with exceptions and minimums). - The parts must be produced immediately and numbered according to the manufacturing sequence. - Tests must be carried out with the machine at operating temperature defined for each use case. - Test parts are to be produced under standard production conditions. - Special specifications if tooling is broken in, ensuring tooling lifetime. - Tooling change and other adjustments during MFI are not allowed unless integrated automatic corrections are involved. - Handling machine malfunctions during MFI, which requires restarting the test. - Specifying the measuring method before investigation, agreed upon by supplier and customer. - Conducting MFI during the production of different parts which may have different characteristics. - **Footnote:** - Indicates the consideration of manual data recording forms' occurrence in practice, mentioning the limitations in such procedures. ### 8. Color Analysis: - The document comprises black text on a white background, facilitating ease of reading with no additional colors present. ### 9. Perspective and Composition: - The layout consists of a standard document format with headings and sections aligned in a readable manner. The information is broken down into sub-sections with clear headings and bullet points for better readability. ### 10. Contextual Significance: - This document likely serves as part of a larger set of guidelines or a standard manual, possibly related to the operation and quality assurance in manufacturing processes. #### Summary: The document provides guidelines for the use of test equipment and sampling procedures in a manufacturing or production quality control setting. Sections are clearly outlined to ensure that all steps and conditions are understandably documented and enforceable. The main content emphasizes the precision, consistency, and specified methodologies necessary for maintaining high production standards. #################### File: VW%2010130_EN%281%29.pdf Page: 25 Context: # 4.3 Special regulation for restricted MFI If the conditions named in 4.2 cannot be met completely, in justified cases a restricted MFI can be carried out, for which special regulations are to be agreed upon between supplier and customer and documented under the note "Restricted MFI." # 4.4 Data analysis ## 4.4.1 Selection of the expected distribution model The expected distribution model depends on the characteristic type. For the most important types of characteristics (see also VW 01056), the assigned distribution models are to be taken from Table 2. ## Table 2 - Assignment of characteristic types and distribution models | Characteristic Type | Distribution Model | |------------------------------|--------------------| | Length dimensions | N | | Diameter, radius | N | | Straightness | B1 | | Flatness | B1 | | Roundness | B1 | | Cylindricity | B1 | | Profile of any line | B1 | | Profile of any surface | B1 | | Parallelism | B1 | | Squareness | B1 | | Slope (angularity) | B1 | | Position | B2 | | Coaxiality/concentricity | B2 | | Symmetry | B1 | | Radial runout | B2 | | Axial runout | B2 | | Roughness | B1 | | Unbalance | B2 | | Torque | N | **Legend:** - N: Normal distribution - B1: Type I absolute value distribution - B2: Type II absolute value distribution (Rayleigh distribution) For characteristic types not listed, in most cases an assignment of a distribution can be carried out according to the following rules: - A normal distribution for characteristics with two-sided tolerance zones or one-sided tolerance zone only - And a type I or II absolute value distribution for characteristics with one-sided tolerance zone only Image Analysis: ### Image Analysis **Image 1** #### Localization and Attribution - **Image:** Page 25 of a document labeled "VW 101 30: 2005-02". #### Text Analysis 1. **Headers and Subheaders:** - **4.3 Special regulation for restricted MFI:** Describes conditions under which a restricted MFI can be carried out when certain criteria cannot be met, requiring agreed-upon regulations between supplier and customer. - **4.4 Data analysis:** Introduces processes related to data analysis. - **4.4.1 Selection of the expected distribution model:** Provides guidelines on choosing the appropriate distribution model for characteristic types. 2. **Body Text:** - **Special regulation for restricted MFI:** If conditions named in 4.2 cannot be met, justified cases allow for a restricted MFI, agreed upon between supplier and customer under the note "Restricted MFI." - **Selection of the expected distribution model:** Assigned distribution models based on characteristic type are to be taken from Table 2 and depend on the characteristic type. #### Diagram and Chart Analysis 1. **Table 2: Assignment of characteristic types and distribution models:** - **Characteristic Types:** - Length dimensions - Diameter, radius - Straightness - Flatness - Roundness - Cylindricity - Profile of any line - Profile of any surface - Parallelism - Squareness - Slope (angularity) - Position - Coaxiality/concentricity - Symmetry - Radial runout - Axial runout - Roughness - Unbalance - Torque - **Distribution Models:** - N: Normal distribution - B1: Type I absolute value distribution - B2: Type II absolute value distribution (Rayleigh distribution) 2. **Legend Explanation:** - **N:** Normal distribution - **B1:** Type I absolute value distribution - **B2:** Type II absolute value distribution (Rayleigh distribution) #### Contextual Significance - **Overall Document:** This page is part of a technical document, likely a standards or protocol document for automotive manufacturing or engineering. - **Purpose:** Provides guidance on special regulations and expected distribution models for various characteristic types important for mechanical or manufacturing quality control. #### Perspective and Composition - **Perspective:** The image appears to be a straight-on snapshot of a document page. - **Composition:** Text is organized into sections with clear headings, subheadings, and a table for visual clarity. ### Summary The analyzed visual content consists of a documented page detailing regulations and data analysis related to characteristic types in the context of a manufacturing or engineering standard. The page discusses restricted MFI conditions, the selection of expected distribution models, and the assignment of characteristic types according to their distribution model in a structured and clear manner. The table and legend enhance understanding by providing specific classifications and explanations. #################### File: VW%2010130_EN%281%29.pdf Page: 26 Context: # 4.4.2 Test for outliers First, a determination of whether the measured values recorded contain outliers is made using the distribution-free detector test according to VW 101 33. Outliers are measured values that lie so far from the other measured values that it is highly probable that they do not come from the same population as the remaining values, e.g., erroneous measurements. The outlier test shall be carried out with a confidence level of 99%. ## 4.4.3 Take outliers out of the calculation of statistics If outliers are identified, these are not considered in the calculation of the statistics. However, the outliers shall not be deleted. Rather, they shall be marked accordingly in the graphic representation of the single value curve and their number shall be indicated in the documentation. ### 4.4.4 Test for change of the production location Using the distribution-free Run Test according to Swed-Eisenhard (see [1]), a determination shall be made of whether the production location has changed systematically during the sampling. A systematic change of the production location can occur, e.g., due to the influence of temperature or due to tooling wear (trend curve). This test shall be carried out with a confidence level of 95%. If only the frequency distribution of classified measured values was recorded, this test cannot be used. #### 4.4.5 Test for deviation from the specified distribution model The recorded measured values are to be tested to see whether they exhibit a significant deviation from the distribution model that was defined for the characteristic involved. To do this, in the case of a specified normal distribution, the Epps-Pulley test (see ISO 5479) shall be used and in the case of a different specified model, e.g., with a type I or II absolute value distribution, the chi-square test (see [1]) shall be used with a confidence level of 95%. A deviation from the specified distribution model can occur, e.g., due to different material batches during the sampling (mixed distribution, see example 3 in Section 5). A deviation from the specified distribution model can occur, e.g., due to sampling from different tools (mixed distribution, see also Section 3, in Figure 5). ##### 4.4.6 Evaluation according to normal distribution In the case of a specified normal distribution or one that is approximated according to criteria (1.13), (1.22), in which the measured values do not exhibit any significant deviation from the distribution model, the calculation of the capability indices is carried out according to formulas (2.1) to (2.5), depending on the tolerancing, whereby the dispersion range limits are determined according to (2.6). ###### 4.4.7 Evaluation according to specified model In the case of a different specified distribution model, e.g., type I or II absolute value distribution, in which the measured values do not exhibit any significant deviation from the distribution model, the calculation of the capability indexes are carried out according to formulas (2.1) to (2.5), whereby the statistics of the distribution to be fitted are determined according to formulas (2.15) and (2.16) or (2.24) and (2.25) respectively with the use of the approximated function (2.18) or (2.27) respectively and the dispersion range limits can be calculated according to the approximated functions (2.19) or (2.28) respectively. Image Analysis: ### Analysis of the Visual Content **Aspect 1: Localization and Attribution** - The provided content appears to be a page from a document, labeled as "Page 26," and originates from "VW 101 30: 2005-02." **Aspect 4: Text Analysis** - The document includes several textual sections, each elaborating on different aspects of statistical tests relevant to quality assessments in manufacturing or engineering contexts. The identified sections are: 1. **Test for outliers (4.4.2):** - Discusses how to determine if measured values contain outliers using a distribution-free test method according to VW 101 33. - Outliers are measured values that significantly differ from others, indicating possible errors. 2. **Take outliers out of the calculation of statistics (4.4.3):** - States that outliers should not be removed but marked accordingly in graphic representations. 3. **Test for change of the production location (4.4.4):** - Indicates the use of the distribution-free Run Test to determine if the production location has changed systematically due to sampling. - The test checks for changes due to various factors like tooling wear or temperature influence. 4. **Test for deviation from the specified distribution model (4.4.5):** - Describes a process to test if values deviate significantly from a specified distribution model. - Different methodologies are noted, such as the Epps-Pulley test for normal distribution and the chi-square test for other models. 5. **Evaluation according to normal distribution (4.4.6):** - Specifies the evaluation of capability indexes when values don't significantly deviate from a specified normal distribution. 6. **Evaluation according to specified model (4.4.7):** - Details on evaluating capability indexes when values don't significantly deviate from a specified model different from the normal distribution. **Aspect 11: Metadata Analysis** - The metadata reveals the document type and standardized reference, indicating it is likely part of a technical or industrial standard specific to VW (Volkswagen) for quality assessment or testing procedures, dated 2005-02. **Aspect 12: Graph and Trend Analysis** - Although the page analyzed does not contain any graphical elements or data trends, it provides a detailed explanation of how such analyses should be carried out per the described methods. **Aspect 13: Graph Numbers** - There are references to various formulas and sections that seem to contain mathematical formulations/details about the mentioned tests: - Formulas (2.1) to (2.5), (2.15), (2.16), (2.18), (2.19), (2.24), (2.25), (2.27) and (2.28). - Example references can be found in sections 3 and 5, as well as Figure 5. **Aspect: Ablaufprozesse (Process Flows)** - The document describes specific statistical testing flows: - Identification of outliers. - Inclusion/exclusion in statistical calculations. - Testing for production location changes. - Assessing deviations from distribution models. - Evaluation based on normal distribution and specific models. **Aspect: Prozessbeschreibungen (Process Descriptions)** - **Test for outliers:** Process of identifying outliers using VW standard methods. - **Run Test for production location:** A statistical test to identify systematic changes in production settings. - **Epps-Pulley/Chi-square Tests:** Specific statistical tests to identify deviations from distribution models. - **Evaluation Processes:** Methods for evaluating using normal distribution models and specified non-normal distribution models. **Conclusion** The provided text is highly technical, focusing on methods for identifying and analyzing statistical anomalies and testing in the production and manufacturing context. The detailed descriptions and references to specific statistical processes imply its usage for quality control and ensuring product consistency. #################### File: VW%2010130_EN%281%29.pdf Page: 27 Context: # 4.4.8 Distribution-free evaluation If the statistical test results in a contradiction between the recorded measured values and the specified distribution model, or if not fitting distribution model can be found for the considered production characteristic, a distribution-free calculation of the capability indexes is carried out according to formulas (2.29) to (2.40). # 4.5 Documentation The documentation of an MFI regarding a characteristic must contain the following information and representations: ## Header data: - Department, coordinator and preparation date - Information regarding the part - Designation, nominal dimension and tolerance of the characteristic - Machine data - Test equipment data - Production time period ## Results: - Graphical representation of the single value curve with the random sample mean values with limit lines of the tolerance zone (as long as single values were recorded) - Histogram with a fitted distribution model, limit lines of the tolerance zone and dispersion range, as well as mean value and/or median value line - Representation in the probability grid with the fitted distribution model, limit lines of the tolerance zone and dispersion range, as well as mean value and/or median value line (see [2]) - Number of measured values - Number of measured values evaluated or outliers found - Estimated value of the production location - Estimated values of the dispersion range limits or the estimated value of the dispersion range - The distribution model used - The result of the test for change of the production location - The result of the test for deviation from the specified distribution model - Calculated capability indexes Cm and Cmk (to two digits after the decimal) - Required limit values for Cm and Cmk ## References and notes: - If necessary, reference to restricted MFI - If necessary, special agreements between supplier and customer - If necessary, special events during the sampling Image Analysis: ### 1. Localization and Attribution: - Document consists of a single page numbered Page 27. - No images to be numbered or located; text-based document. ### 4. Text Analysis: - **Heading:** The main heading is "4.4.8 Distribution-free evaluation" followed by a subheading "4.5 Documentation." - **Content:** - **4.4.8 Distribution-free evaluation:** Describes the process when statistical test results contradict recorded measured values or specified distribution models and calls for a distribution-free calculation of capability indexes. - **4.5 Documentation:** Outlines the required documentation for an MFI regarding a characteristic, detailing various types of required information and representations. - **Header Data:** Mention of several required details including department, coordinator, preparation date, and machine data. - **Results:** List of results that need to be documented, such as graphical representations, number of measured values, and calculated capability indexes. - **References and notes:** Highlights special considerations such as referencing restricted MFI and agreements between supplier and customer. **Significance:** - This section defines comprehensive criteria for evaluating statistical data and documenting it in a manufacturing or production environment. The text’s emphasis on detailed documentation ensures consistency, accuracy, and accountability in reporting measurements and test results. ### 9. Perspective and Composition: - **Perspective:** The document is presented from a standard top-down viewpoint, typical for technical manuals or guidelines. - **Composition:** The text is formatted in a structured manner with headings and subheadings to separate sections clearly. Bullet points are used to enumerate required data and results, making the information easily scannable and organized. ### 10. Contextual Significance: - **Context in Document:** This text serves as a guideline for documenting measurement data and test results in detail to facilitate quality control and process validation. - **Overall Message:** Ensures the accuracy and reliability of production data reporting, critical for maintaining and improving product quality and manufacturing efficiency. ### 14. Prozessbeschreibungen (Process Descriptions): - **Documentation of Measurement Data:** - Record fixed header data like department, coordinator, preparation date, machine data, etc. - Document results including graphical representations and statistical data points such as mean values, tolerance ranges, etc. - Note special considerations and required references as needed. - Purpose is to create a thorough record for quality assurance and validation. This document serves as a technical procedural guide to manage and document measurement data and its evaluation systematically. #################### File: VW%2010130_EN%281%29.pdf Page: 28 Context: # 4.6 Results Evaluation Whether a machine can be evaluated capable with respect to production of a considered characteristic depends on the following result evaluation: - If outliers occur during an evaluation, their cause has to be clarified. Outliers shall only be caused by incorrect measurements or be wrongly identified as such using the outlier test based on the specified probability of error of 1%. Otherwise, the machine shall be evaluated as incapable. If more than 5% of the recorded measured values or more than 2 values are identified as outliers, there shall be a test of whether the test process is faulty. Then the MFI is to be repeated if necessary. - If the production location has changed significantly during the sampling, generally its cause has to be known and the effect has to be acceptable in order to meet the requirement for machine capability (see last paragraph of this section for exception). - If a distribution-free evaluation exists due to a significant deviation from the specified distribution model and if no other distribution model can be assigned to the considered characteristic without contradiction, the cause must be known and the effect must be acceptable³, in order to meet the requirement for machine capability (see last paragraph of this section for exception). Unless otherwise agreed, the capability indexes determined with an effective random sample size of \( n_e \geq 50 \) (i.e. without outliers) must meet the requirement: \[ \bar{C}_m \geq 2.0 \quad \text{and} \quad \bar{C}_{pk} \geq 1.67 \quad \text{for a characteristic with two-sided tolerance zones} \] \[ \bar{C}_{pk} \geq 1.67 \quad \text{for a characteristic with one-sided tolerance zone only} \] in order for the machine to be evaluated as capable. In this case, for comparison to the limit values, the capability indexes determined are to be rounded to two digits after the decimal so that, e.g., a determined value of \( \bar{C}_{pk} = 1.66545 \) will still meet the requirement after the resulting rounding to 1.67. With an effective random sample size of \( 20 \leq n < 50 \), correspondingly higher limit values shall be complied with. The fitted limit values are given in Table 3 for a few random sample sizes. If there is agreement on other limit values on the basis of \( n_e \geq 50 \), the corresponding fitted limit values are to be determined according to formulas (3.7) to (3.9). ### Table 3 - Limit Values for Machine Capability for \( 20 \leq n \leq 50 \) | \( n_e \) | \( \bar{C}_m \geq \) | \( \bar{C}_{pk} \geq \) | |-----------|----------------------|--------------------------| | 20 | 2.28 | 1.93 | | 25 | 2.19 | 1.85 | | 30 | 2.13 | 1.79 | | 35 | 2.08 | 1.75 | | 40 | 2.05 | 1.72 | | 45 | 2.02 | 1.69 | | 50 | 2.00 | 1.67 | If a capability index results that is lower than the corresponding limit value, the machine is to be evaluated as incapable. Image Analysis: ### Comprehensive Examination of Visual Content #### Localization and Attribution: 1. **Image Location**: The entire content is contained within a single continuous page. 2. **Image Number**: Image 1. #### Text Analysis: 1. **Extracted Text**: - **Title**: "4.6 Results evaluation" - Detailed explanation discussing the evaluation of machine capability, the handling of outliers, and the conditions under which a machine can be considered capable. - Conditions for outliers and distribution-free evaluation. - Requirements for effective random sample sizes, specified capability indexes, and tolerance zones. - **Table**: "Table 3 - Limit values for machine capability for 20 ≤ ne ≤ 50" - **Table Values**: - For [nₑ = 20]: ĉₚ ≥ 2.28, ĉₚₖ ≥ 1.93 - For [nₑ = 25]: ĉₚ ≥ 2.19, ĉₚₖ ≥ 1.85 - For [nₑ = 30]: ĉₚ ≥ 2.13, ĉₚₖ ≥ 1.79 - For [nₑ = 35]: ĉₚ ≥ 2.08, ĉₚₖ ≥ 1.75 - For [nₑ = 40]: ĉₚ ≥ 2.05, ĉₚₖ ≥ 1.72 - For [nₑ = 45]: ĉₚ ≥ 2.02, ĉₚₖ ≥ 1.69 - For [nₑ = 50]: ĉₚ ≥ 2.00, ĉₚₖ ≥ 1.67 - Footnotes and references to formulas and paragraphs. #### Diagram and Chart Analysis: 1. **Table Analysis**: - **Title**: "Table 3 - Limit values for machine capability for 20 ≤ nₑ ≤ 50" - Presents the fitted limit values for machine capability indexes (ĉₚ and ĉₚₖ) for different effective sample sizes (nₑ). - **Axes**: No graphical axes as it is a table. - **Key Insights**: - For smaller sample sizes, the required capability indexes are higher. - As the sample size increases, the limit values for ĉₚ and ĉₚₖ decrease. #### Ablaufsprozesse (Process Flows): 1. **Process Flow Description**: - The process flow involves evaluating a machine's production capability considering specific criteria (outliers, production location changes, distribution-free evaluation). - The overall flow hinges on monitoring capability indexes and ensuring that the system meets requirements defined by fit limit values based on sample size. #### Prozessbeschreibungen (Process Descriptions): 1. **Description**: - **Outliers Evaluation**: Clarify causes and ensure correct measurements. - **Production Location Changes**: Identify and accept changes if they significantly alter the sampling. - **Distribution-free Evaluation**: Address significant deviations and maintain acceptable fit limit values. - **Capability Indexes Determination**: Calculate and evaluate by rounding to two decimal digits under specified conditions. #### Typen Bezeichnung (Type Designations): 1. **Types/Categories**: - **Two-sided Tolerance Zones**: Capability index values ĉₚ ≥ 2.20, ĉₚₖ ≥ 1.67 required. - **One-sided Tolerance Zones**: Capability index value ĉₚₖ ≥ 1.67 required. #### Trend and Interpretation: 1. **Identified Trends**: - Higher sample sizes result in slightly relaxed capability index values. 2. **Interpretation**: - Ensuring machine capability through rigorous distribution and outlier checks indicates a gradually stable and reliable production setup with increased sample sizes, leading to relaxation in capability indexes. #### Contextual Significance: 1. **Analysis in Document Context**: - This section is likely part of a larger technical standard (VW 101 30: 2005-02) and provides crucial guidelines for evaluating machine capability. - It ensures uniformity and reliability in production by adhering to the defined capability indexes. #### Anomaly Detection: 1. **Identified Anomalies**: None detected within the provided content. #### Perspective and Composition: 1. **Description**: - The page is laid out in a standard technical document format, with headers, paragraphs, and a table that outlines detailed specifications and guidelines. By analyzing these various aspects of the visual content, the document provides thorough guidelines on evaluating machine capability, emphasizing the importance of outlier analysis, impact of production changes, and maintaining acceptable capability indexes across specific sample sizes. #################### File: VW%2010130_EN%281%29.pdf Page: 29 Context: With a determined capability index of \( c_{mk} \geq 2.33 \) (corresponds to 14 σ) and additionally \( c_{p} \geq 2.67 \) (corresponds to 16 σ) for characteristics with two-sided tolerance zones, the machine can be evaluated as capable with respect to the considered characteristic, even independent of a significant location change or deviation from the specified distribution model. ## 4.7 Machine Optimization For the case where the machine capability cannot be documented with respect to the tested characteristic, measures for machine optimization are necessary. To do this, the corresponding influences are to be identified (e.g., using ODE statistical test methodology) and eliminated. ## 4.8 Handling Incapable Machines If it is not possible to achieve machine capability with machine optimizations that are economically reasonable, there shall first be an investigation using statistical tolerance calculation according to VW 01057 of whether a tolerance extension is possible to achieve the machine capability. If machine capability cannot be achieved using these measures, a decision is to be made whether the machine will be accepted according to special regulations agreed upon in writing or not. These special regulations shall contain the following points: - Reasons for the acceptance - Risk and cost considerations - If necessary, restricting production and additional test conditions - Specification of the responsibility Image Analysis: ### Comprehensive Examination of the Visual Content **Image 1:** 1. **Localization and Attribution:** - This document is a single-page text. - Identified as Image 1. 2. **Text Analysis:** - Title: "VW 101 30: 2005-02" - The main body text includes sections titled "4.7 Machine optimization" and "4.8 Handling incapable machines." **Section: 4.7 Machine optimization** - Content: Discusses measures necessary for machine optimization if the machine capability cannot be documented with respect to the tested characteristic. - Significance: Emphasizes the importance of identifying and eliminating influences to achieve machine optimization. **Section: 4.8 Handling incapable machines** - Content: Discusses steps to take if machine capability cannot be achieved through optimization. It outlines the need for statistical tolerance calculation and lists the points to be included in special regulations. - Significance: Highlights the procedural steps for dealing with incapable machines, ensuring compliance with VW standards and guidelines. - Bulleted points: - Reasons for the acceptance - Risk and cost considerations - If necessary, restricting production and additional test conditions - Specification of the responsibility The content in these sections is focused on maintaining and ensuring the capability of machines within specified tolerance zones. **Contextual Significance:** - This page is likely part of a technical or operational manual, possibly a standard document specifying procedures and standards for machine capability and optimization. - It contributes to the overall theme of maintaining stringent quality and operational standards. **Perspective and Composition:** - The document has a standard text-based format typical of technical guidelines or standards. - The composition is straightforward, with headings and bullet points for ease of understanding and reference. This concludes the analysis of Image 1. The visual and textual content provides detailed procedural information regarding machine optimization and handling incapable machines, following VW standards. #################### File: VW%2010130_EN%281%29.pdf Page: 30 Context: # 5 Examples ## Example 1: Shaft diameter with a nominal dimension of 20 mm, a lower limiting value of \( G_{u} = 19.7 \) mm and an upper limiting value of \( G_{l} = 20.3 \) mm. Using the statistical tests, no outliers resulted, no significant change of the production location occurred and there was no significant deviation from an expected normal distribution from \( n = 50 \) measured values of the random sample. The following random sample statistics are determined: \[ \bar{x} = 20.05 \quad \text{and} \quad \bar{s} = 0.05 \] Therefore, according to formula (2.11), the following estimated values of the dispersion range limits result for the normally distributed populations: \[ \hat{x}_{0.135\%} = \bar{x} - 3 \cdot \bar{s} = (20.05 - 3 \cdot 0.05) \text{ mm} = 19.9 \text{ mm} \] \[ \hat{x}_{99.865\%} = \bar{x} + 3 \cdot \bar{s} = (20.05 + 3 \cdot 0.05) \text{ mm} = 20.2 \text{ mm} \] And from that, ultimately, the following capability indexes result: \[ \bar{c}_{m} = \frac{G_{u} - G_{l}}{\hat{x}_{99.865\%} - \hat{x}_{0.135\%}} = \frac{20.3 - 19.7}{20.2 - 19.9} = \frac{0.6}{0.3} = 2.0 \] \[ \bar{c}_{k} = \min \left( \frac{G_{u} - \bar{x}}{\hat{x}_{99.865\%} - \bar{x}} , \frac{\bar{x} - G_{l}}{\bar{x} - \hat{x}_{0.135\%}} \right) = \min \left( \frac{20.3 - 20.05}{20.2 - 20.05}, \frac{20.05 - 19.7}{20.05 - 19.9} \right) = \min \left( \frac{0.25}{0.15}, \frac{0.35}{0.15} \right) = \frac{20.3 - 20.05}{20.2 - 20.05} = 1.67 \] Because of the capability indexes, it is thus verified that the machine just meets the capability requirements with respect to the considered shaft diameters. Figure 12 shows the evaluation result: ![Figure 12 - Example of a production with the model of a normal distribution and the capability indexes \( c_{m} = 2.0 \) and \( c_{k} = 1.67 \)](url) Image Analysis: ### Analysis of the Visual Content #### 1. **Localization and Attribution:** - The single image located on the page can be referred to as **Image 1**. #### 2. **Object Detection and Classification:** - **Image 1:** - **Objects Detected:** - Text on the upper portion of the image. - A graph on the lower portion of the image. #### 3. **Scene and Activity Analysis:** - **Image 1:** - **Scene:** - The image presents an example related to statistical measurements for production consistency, specifically focusing on shaft diameter. - **Activities:** - The image illustrates the process of calculating and evaluating statistical metrics to verify production quality, including capability indices. #### 4. **Text Analysis:** - **Image 1:** - **Text Extracted:** - "Page 30 VW 101 30: 2005-02" - "5 Examples Example 1: Shaft diameter with a nominal dimension of 20 mm, a lower limiting value of GL = 19.7 mm and an upper limiting value of GU = 20.3 mm Using the statistical tests, no outliers resulted, no significant change of the production location occurred and there was no significant deviation from an expected normal distribution from n = 50 measured values of the random sample. The following random sample statistics are determined: z̄ = z̄ = 20,05 and d = s = 0,05 ... etc." - **Significance:** - The text provides a detailed description of a statistical analysis example for the production of shafts, describing the calculation of capability indices and their importance in quality control. #### 5. **Diagram and Chart Analysis:** - **Image 1:** - **Graph:** - **Axes:** - X-axis: Measured value (ranges from 19.70 to 20.30) - Y-axis: Frequency (no specific scale values provided) - **Data:** - Plot shows a distribution of measured shaft diameters with a mean value around 20.05. - Indicated points on the horizontal axis: x̂0.135% and x̂99.865% - **Legend:** - GL: 19.7 mm - GU: 20.3 mm - **Key Insights:** - The graph demonstrates a normal distribution of measured shaft diameters, with calculated indices \(c_m\) and \(c_{mk}\) to validate compliance with production standards. #### 6. **Product Analysis:** - **Image 1:** - **Product:** Shaft with a nominal diameter of 20 mm. - **Key Features:** - Measurement range: 19.7 mm to 20.3 mm. - Mean value: 20.05 mm. - Standard deviation: 0.05 mm. #### 7. **Anomaly Detection:** - **Image 1:** - **Anomalies:** - No anomalies detected in the data or presentation. #### 8. **Color Analysis:** - **Image 1:** - **Dominant Colors:** - The image utilizes shades of black, grey, and white. - **Impact:** - The neutral color scheme emphasizes clarity and professionalism, appropriate for a technical document. #### 9. **Perspective and Composition:** - **Image 1:** - **Perspective:** - The text is presented in a straightforward, document-style format. - The graph is shown from a straight-on perspective, typical of technical visualizations. - **Composition:** - Structured into two main sections: descriptive text above and an illustrative graph below. #### 10. **Contextual Significance:** - **Image 1:** - **Overall Context:** - The image is part of a technical document, likely related to quality control in manufacturing. - **Contribution:** - The image offers practical examples of statistical quality assessment methods, enhancing understanding of the theoretical concepts discussed in the document. #### 12. **Graph and Trend Analysis:** - **Image 1:** - **Trend Analysis:** - The normal distribution curve indicates that the production process is consistent and within specified limits. - **Interpretation:** - Capability indices \(c_m\) and \(c_{mk}\) confirm that the process meets the required quality standards. #### 14. **Tables:** - **Image 1:** - No tables are included in the image. #### 15. **Ablaufprozesse (Process Flows):** - **Image 1:** - Describes the process of calculating and verifying statistical capability indices. #### 16. **Prozessbeschreibungen (Process Descriptions):** - **Image 1:** - Detailed process for statistical evaluation of shaft diameters involving calculating dispersal limits and capability indices using specific formulas. #### 18. **Trend and Interpretation:** - **Image 1:** - **Trend:** - The production process is stable and meets quality requirements as demonstrated by capability indices. - **Interpretation:** - The normal distribution of data suggests a well-controlled production process. In summary, the image provides a clear example of using statistical methods to ensure manufacturing quality, supported by detailed textual explanations and an illustrative graph. #################### File: VW%2010130_EN%281%29.pdf Page: 31 Context: # Example 2 **Hole with a maximum permissible position deviation of \( G_o = 0.2 \, \text{mm} \)** From the \( n = 50 \) measurements of the random sample, the statistical tests did not result in any outliers, no significant location change, and no significant deviation from an expected type II absolute value distribution. The following random sample statistics were determined: \[ \hat{x} = 0.038 \, \text{mm} \quad \text{and} \quad s = 0.02 \, \text{mm} \] The random sample statistics result in the ratio: \[ \frac{\hat{x} - G_o}{s} = \frac{0.038 - 0.02}{0.02} = 1.9 \] Since, because of the random dispersion of the random sample statistics, this value is lower than the limit value 1.9131 according to condition (2.23), the ratio is set to this limit value, which in turn results in an eccentricity of \( z = 0 \). In this way, the second parameter value of the type II absolute value distribution to be fitted is calculated according to special case (2.26) as follows: \[ \sigma_{N_{99.865}} = 1.526 - \hat{x} = 1.526 - 0.038 = 0.305 \, \text{mm} \] The estimated values of the dispersion range limits result from formula (2.27): \[ \hat{x}_{0.135} = 0.0773 - \sigma \cdot 0.0773 \cdot 0.02 \, \text{mm} = 0.0016 \, \text{mm} \] Finally, according to formulas (2.3) and (2.4), the following capability indexes result: \[ \hat{C}_{p} = \frac{G_o}{s} = \frac{0.2}{0.111 - 0.0016} = 1.83 \] \[ \hat{C}_{mk} = \frac{G_o - \hat{x}}{s} = \frac{0.2 - 0.038}{0.111 - 0.038} = 2.22 \] Figure 13 illustrates the evaluation result. ## Figure 13 - Example of a production with the model of a type II absolute value distribution and the capability indexes \( \hat{C}_{p} = 1.83 \) and \( \hat{C}_{mk} = 2.22 \) Because of the determined statistic \( C_{mk} \), it is verified that the machine meets the requirement well with respect to the position deviation of a hole. Although no limit value is specified for statistic \( C_{mk} \) in the case with an upper limited tolerance zone, comparison to the \( C_{mk} \) value provides information on the production location and the smaller \( C_{mk} \) value indicates that the location lies closer to the natural limit zero than to the upper limiting value. Image Analysis: ### Analysis of the Visual Content in Detail: --- #### 1. **Localization and Attribution:** - **Image 1:** - Present on the lower part of the page. - Referred to as "Figure 13" in the document. #### 3. **Scene and Activity Analysis:** - **Image 1:** - The scene depicts a graph titled "Figure 13 - Example of a production with the model of a type II absolute value distribution and the capability indexes \( \hat{c}_{m} = 1.83 \) and \( \hat{c}_{mk} = 2.22 \)". - The graph shows the measured values on the x-axis and the frequency on the y-axis, illustrating the statistical distribution of a production process. #### 4. **Text Analysis:** - The text describes a statistical analysis conducted on a sample with a maximum permissible position deviation of \( G_0 = 0.2 \) mm. - Key excerpts: - "Hole with a maximum permissible position deviation of \( G_0 = 0.2 \) mm." - "From the n = 50 measurements of the random sample, the statistical tests did not result in any outliers, no significant location change and no significant deviation from an expected type II absolute value distribution. The following random sample statistics were determined:..." - Detailed calculations and results about second parameter values, dispersion range limits, and capability indexes \( \hat{c}_{m} \) and \( \hat{c}_{mk} \). - Significance: These details explain the statistical validation of the production process, ensuring that it meets the specified tolerances and quality requirements. #### 5. **Diagram and Chart Analysis:** - **Image 1:** - The graph shows the distribution of measured values of a production sample. - **Axes and Scales:** - X-axis (Measured Value): 0 to 0.20 with intervals marked at every 0.02. - Y-axis (Frequency): Represents the frequency of measurements within each interval. - **Legend and Key Insights:** - Dispersion range limits \( \hat{x}_{0.135} \) and \( \hat{x}_{0.865} \) are marked. - The peak of the distribution is around \( 0.03 \), indicating the most frequent measurement intervals. - The graph illustrates that the majority of measurements fall within the acceptable range defined by the capability indexes, validating the production quality. #### 6. **Product Analysis:** - The document details the statistical quality control process for a production sample, emphasizing how the measurements conform to specified tolerances. #### 8. **Color Analysis:** - **Image 1:** - Dominant Colors: Black and shades of grey. - Impact: The use of monochrome colors, with black lines and grey shading, adds to the formal and technical appearance, emphasizing the accuracy and precision of the information presented. #### 9. **Perspective and Composition:** - **Image 1:** - Perspective: The graph uses a standard front-facing view. - Composition: The elements are neatly arranged with clearly labeled axes, ensuring the data is easily interpretable. The key points such as \( \hat{x}_{0.135} \), \( G_0 \), and \( \hat{x}_{0.865} \) are highlighted for clarity. #### 13. **Graph Numbers:** - **Image 1:** - **Data Points:** - \( 0.021 \), \( 0.036 \), \( 0.053 \), \( 0.065 \), etc., on the X-axis representing the measured values. - Frequency corresponding to each interval is depicted by the height of the bars on the Y-axis. #### **Ablaufprozesse (Process Flows):** - The text details the process flow of statistical measurement and evaluation for the production quality control, including the determination of capability indexes and deviation limits. #### **Prozessbeschreibungen (Process Descriptions):** - Describes the statistical methods used for evaluating a production process, including formulas and results for dispersion range limits and capability indexes. #### **Trend and Interpretation:** - The measurements show a consistent trend within the defined acceptable range, with few outliers, demonstrating a stable and controlled production process that meets specified quality standards. #### **Tables:** - Although there is no distinct table, the textual content and diagram combine to present detailed statistical data about the production sample. This visual content provides a thorough statistical analysis of a production process, confirming the quality and consistency of the manufacturing outcomes. #################### File: VW%2010130_EN%281%29.pdf Page: 32 Context: # Example 3: Shaft diameter with a nominal dimension of 20 mm, a lower limiting value of \( G_e = 19.7 \) mm and an upper limiting value of \( G_u = 20.3 \) mm. From \( n = 50 \) measured values of the random sample, due to the statistical tests, no outliers resulted and no significant location change resulted, but a significant deviation from an expected normal distribution did. Therefore, a distribution-free evaluation is carried out according to Section 3.22. To do so, the following random sample statistics were determined: \[ \bar{x}_{50\%} = \bar{x} = 20.02 \, \text{mm}, \, x_{max} = 20.19 \, \text{mm} \, \text{and} \, x_{min} = 19.85 \, \text{mm} \] Correction factor according to formula (2.38) and Table 1: \[ k = \frac{6}{d_d} = \frac{6}{4.5} = 1.33 \] Range according to formula (2.37): \[ R = x_{max} - x_{min} = 20.19 - 19.85 = 0.34 \, \text{mm} \] According to formula (2.36): \[ x_c = \frac{x_{max} + x_{min}}{2} = \frac{20.19 + 19.85}{2} = 20.02 \, \text{mm} \] Estimated values for dispersion range limits according to formula (2.35): \[ \begin{align*} \hat{x}_{L} &= x_c - k \frac{R}{2} = 20.02 - 1.33 \frac{0.34}{2} = \frac{20.246}{19.794} \, \text{mm} \\ \hat{x}_{U} &= x_c + k \frac{R}{2} = 20.02 + 1.33 \frac{0.34}{2} = \frac{20.246}{19.794} \, \text{mm} \end{align*} \] Thus the formulas (2.29) and (2.30) resulted in the capability indexes: \[ \bar{c}_m = \frac{G_u - G_L}{\bar{x} - \hat{x}_{L}} = \frac{20.3 - 19.7}{20.02 - 20.246} = 1.33 \] \[ \bar{c}_{mk} = \min \left( \frac{G_u - \bar{x}_{50\%}}{\bar{x}_{50\%} - \hat{x}_{L}}, \frac{G_L - \bar{x}_{50\%}}{\bar{x}_{50\%} - \hat{x}_{U}} \right) = \frac{20.3 - 20.02}{20.246 - 20.02} = 1.24 \] Figure 14 illustrates the evaluation result. ## Example 14 - Example of a production without defined distribution model with the capability indexes \( c_{m} = 1.33 \) and \( c_{mk} = 1.24 \) From the capability indexes determined, it can be seen that the machine does not meet the capability requirement with respect to the considered characteristic. The significant deviation from an expected normal distribution supplies interesting information in this context. Because of this, an optimization potential can be recognized, in this case through mixed distribution. Image Analysis: ### Visual Content Analysis #### Image Details: 1. **Localization and Attribution:** - **Image 1**: There is only one image present on the page. 2. **Object Detection and Classification:** - The image features a histogram chart, several numerical calculations, and statistical data. Key elements include text, a bar graph, and mathematical formulas. 3. **Scene and Activity Analysis:** - The scene depicts a technical/engineering document with a focus on statistical analysis and capability evaluation. The activities involve mathematical and statistical examination related to production measures. 4. **Text Analysis:** - The text in the image provides a detailed explanation of statistical calculations for a shaft diameter. Key excerpts include: - "Example 3:" At the beginning, it describes a problem statement involving various measures and statistical tolerance limits. - Several formulas and calculations are displayed. - Example 14 provides an evaluation result and showcases the graph/histogram. - Annotated text at the bottom explains the significance of capability indexes c_m and c_mk, and provides conclusions based on the analysis. 5. **Chart Analysis:** - The image features a bar graph (Histogram) representing the frequency distribution of measured values. - **Axes**: - X-axis: "Measured value" with intervals ranging from 19.75 to 20.25. - Y-axis: "Frequency". - **Data**: The bar heights represent the frequency of occurrence for each range of measured values. - **Insight**: The chart indicates a normal distribution of measured values around the central value, detailing an evaluation on production capability. 6. **Product Analysis:** - The products in discussion are shaft diameters with specific measurements and tolerance limits. - The primary focus is on the production consistency and statistical evaluation of the shaft dimensions. 7. **Anomaly Detection:** - The statistical analysis shows a deviation from the expected normal distribution, suggesting an area for potential optimization, even indicating mixed distribution as a noticeable anomaly. 8. **Color Analysis:** - The document uses monochrome (black and white), a typical color scheme for technical documents to emphasize on clarity and readability of text and graphs. 9. **Perspective and Composition:** - The document is presented from a straightforward, eye-level perspective, typical for technical manuscripts. The composition is logical, with text leading into formulas and culminating in the graphical representation. 10. **Contextual Significance:** - The image and text collectively contribute to the technical evaluation of production quality and highlight the importance of statistical analysis in assessing manufacturing processes. 11. **Graph and Trend Analysis:** - The provided graph emphasizes the distribution of measured shaft diameters. The trend suggests a central tendency but with visible deviations, important for evaluating the machining process capability. 12. **Process Descriptions:** - Detailed process descriptions include calculating correction factors, range, and estimated values for dispersion based on statistical formulas. 13. **Typen Bezeichnung (Type Designations):** - Designations like c_m (Process Capability Index) and c_mk (Corrected Capability Index) are particularly highlighted. Their values denote the precision of the manufacturing process. 14. **Trend and Interpretation:** - The general trend in the analysis shows that while the process is centered around the target measurement, there are variations indicating mixed distributions, a critical point for further quality improvement. ### Summary: This page provides an elaborate statistical analysis related to manufacturing shaft diameters, presenting calculated tolerance limits and capability indexes. The supporting histogram visually complements the textual and numerical analysis, reinforcing the critical need for precision in manufacturing processes. Overall, the document embodies a thorough approach to understanding and optimizing production quality. #################### File: VW%2010130_EN%281%29.pdf Page: 33 Context: # 6 Referenced standards | Standard Code | Description | |---------------|-----------------------------------------------------------------------------------------| | VW 010 56 | Drawings; Form and Position Tolerances | | VW 010 57 | Statistical Tolerance Calculation of Dimension Chains | | VW 101 33 | Test auf Ausreißer (Test for Outliers – currently only available in German) | | DIN 55319 | Quality Capability Statistics (QCS) | | ISO 5479 | Statistical Interpretation of Data - Tests for Departure from the Normal Distribution | # 7 Referenced literature 1. Graf, Henning, Stange, Willich. *Formeln und Tabellen der angewandten mathematischen Statistik*. Springer Publishing Group, third edition, 1987. 2. Küh Meyer, M.. *Statistische Auswertungsmethoden für Ingenieure*. Springer Publishing Group, 2001. 10) In this Section, terminological inconsistencies may occur as the original titles are used. Image Analysis: ### Analysis of the Visual Content: #### Localization and Attribution: - **Image Location and Numbering:** - There is only one image on the page. #### Text Analysis: - **Detected Text:** - The main headings on the page are "6 Referenced standards" and "7 Referenced literature." - The standards listed include: - VW 010 56: Drawings; Form and Position Tolerances - VW 010 57: Statistical Tolerance Calculation of Dimension Chains - VW 101 33: Test auf Ausreißer (Test for Outliers – currently only available in German) - DIN 55319: Quality Capability Statistics (QCS) - ISO 5479: Statistical Interpretation of Data - Tests for Departure from the Normal Distribution - The referenced literature includes: - [1] Graf, Henning, Stange, Willrich, Formeln und Tabellen der angewandten mathematischen Statistik, Springer publishing group, third edition 1987 - [2] Kühlmeyer M., Statistische Auswertungsmethoden für Ingenieure, Springer publishing group, 2001 #### Contextual Significance: - **Overall Document Theme:** - This page seems to be from a technical document related to statistical methods and standards used in engineering or quality management. - The referenced standards and literature indicate a focus on statistical analyses and procedures relevant to precise measurements and quality control in engineering contexts. #### Additional Aspects: - **Ablaufprozesse (Process Flows):** - No process flows depicted. - **Prozessbeschreibungen (Process Descriptions):** - This page does not provide detailed process descriptions but references standards and literature that likely contain relevant processes. - **Typen Bezeichnung (Type Designations):** - The types or categories mentioned are statistical standards and quality control methods (e.g., methods for tolerance calculation, outliers testing). ### Conclusion: This image contains information about standards and literature references relevant to engineering statistical methods and quality control. Specifically, it lists recognized standards and foundational literature that could be pertinent to professionals in the field seeking guidance on measurement tolerances, statistical analyses, and data interpretation. #################### File: VW%2010130_EN%281%29.pdf Page: 34 Context: # 8 Keyword index | Key word | Page | |---------------------------------------|----------| | A | | | Absolute frequency α | 10, 17 | | Absolute cumulative frequency A | 17 | | α-Risk | 20 | | Alternative hypothesis | 20 | | Fitted capability limit values | 19, 28 | | Outlier | 20, 26 | | Confidence level γ | 20, 26 | | B | | | Conditions for the machine capability investigation | 24 | | β-Risk | 20 | | Absolute value distribution, type I | 5, 11 | | Absolute value distribution, type II | 7, 13 | | Machine at operating temperature | 24 | | C | | | Capability | 3 | | Chi-square distribution | 18 | | D | | | Data analysis | 25 | | Density function f(x) | 4 | | Documentation | 27 | | E | | | Restricted machine capability investigation | 25 | | Effective random sample size nₑ | 10, 24 | | Epps-Pulley test | 20, 26 | | Results evaluation | 28 | | Expected value for the w-distribution dₕ | 17 | | Eccentricity z | 7 | | F | | | Determination of capability | 8 | | Capability indexes cₘ and cₜₖ | 3, 9 | | Capability limit values | 18, 28 | | Production location | 3, 28 | | Production variation | 3, 8 | | Production sequence | 24 | | Degree of freedom | 18 | | G | | | Limit values of machine capability | 18, 28 | | H | | | Hampel test | 20 | | Frequency distribution | 10, 17 | | Upper limiting value G₀ | 3, 9 | | I | | | Probability of error α | 20 | Image Analysis: ### Image Analysis **Localization and Attribution:** - **Image Position:** Image 1 - **Image Description:** A page from a document titled "Keyword Index." The document appears to be a technical or academic resource with key terms and their corresponding page numbers. **Text Analysis:** - The text is organized into two main columns: - **Key Word:** Lists specific terms or keywords. - **Page:** Indicates the page numbers where each keyword can be found. **Detected Text:** - **Title and Sections:** - "Page 34" - "VW 101 30: 2005-02" - "8 Keyword index" - **Columns:** - Column 1: "Keyword | Page" - Column 2: Lists of key terms and page numbers. - **Keywords and Page Numbers:** - **A:** - Absolute frequency α: 10, 17 - Absolute cumulative frequency A: 17 - α-Risk: 20 - Alternative hypothesis: 20 - Fitted capability limit values: 19, 28 - Outlier: 20, 26 - Confidence level γ: 20, 26 - **B:** - Conditions for the machine capability investigation: 24 - β-Risk: 20 - Absolute value distribution, type I: 5, 11 - Absolute value distribution, type II: 7, 13 - Machine at operating temperature: 24 - **C:** - Capability: 3 - Chi-square distribution: 18 - **D:** - Data analysis: 25 - Density function f(x): 4 - Documentation: 27 - **E:** - Restricted machine capability investigation: 25 - Effective random sample size nₑ: 10, 24 - Epps-Pulley test: 20, 26 - Results evaluation: 28 - Expected value for the w-distribution dn: 17 - Eccentricity z: 7 - **F:** - Determination of capability: 8 - Capability indexes Cm and Cmk: 3, 9 - Capability limit values: 18, 28 - Production location: 3, 28 - Production variation: 3, 8 - Production sequence: 24 - Degree of freedom: 18 - **G:** - Limit values of machine capability: 18, 28 - **H:** - Hampel test: 20 - Frequency distribution: 10, 17 - Upper limiting value Go: 3, 9 - **I:** - Probability of error α: 20 **Color Analysis:** - **Color Composition:** - The image consists of black text on a white background. - This high contrast makes the text easily readable. **Perspective and Composition:** - **Perspective:** - The image is scanned or photographed from a top-down perspective, showing a flat view of a single page. - The text is well-centered and uniformly spaced. - **Composition:** - The page is laid out in a structured format with two main columns. - The header section indicates the page number and a title. - Keywords on the left are aligned flush, with corresponding page numbers uniformly placed on the right. **Contextual Significance:** - **Overall Context:** - This page appears to be part of a larger technical document or manual. - The keyword index serves as a reference guide, allowing readers to quickly locate specific topics within the document. **Conclusion:** The image is a page from a technical document titled "Keyword Index," which serves as a glossary or reference guide. It is well-organized with keyword terms and their corresponding page numbers, aiding the reader in navigating the document. The monochromatic color scheme, primarily black text on a white background, enhances readability, and the structured layout ensures easy information retrieval. #################### File: VW%2010130_EN%281%29.pdf Page: 35 Context: # Key Word Index | Key Word | Page | |-----------------------------------------------|------| | K | | | Class width Δx | 17 | | Classified measured values | 10, 17 | | Correction factor k | 17 | | L | | | Location | 3 | | M | | | Machine optimization | 29 | | Machine malfunctions | 24 | | Median value | 16 | | Characteristic type | 4, 25 | | Characteristic value | 3 | | Measuring method | 24 | | Lower limiting value Gu | 3, 9 | | Mixed distribution | 26, 32 | | Mean value µ | 4, 10 | | N | | | Normal distribution | 4, 10 | | Null hypothesis | 20 | | Zero offset | 6 | | P | | | Parameter of a distribution | 3 | | Test variable | 20 | | Test value | 20 | | Test equipment use | 24 | | Q | | | Quantile | 9 | | - of the standardized normal distribution | 18 | | - of the chi-square distribution | 18 | | R | | | Rayleigh distribution | 7 | | Radial deviation r | 7 | | Blank batch | 24 | | Rounding of capability values | 28 | | Run test | 20 | | S | | | Estimation / estimated value | 8, 9 | | Threshold value | 20 | | Standard production conditions | 24 | | Significant change / deviations | 20 | | Range R | 17 | | Standard deviation σ | 4, 10 | | Standardized normal distribution | 5 | | - U Transformation | 5 | | - Distribution function Φ(μ₁) | 5 | | - Probability density function φ(u) | 5 | | Statistical tests | 20 | | Statistical tolerance calculation | 29 | Image Analysis: ### Analysis of Visual Content #### **1. Localization and Attribution:** - The provided visual content is a single page (Page 35) from a document titled "VW 101 30: 2005-02." - Since there is only one image on the page, we'll denote it as **Image 1**. #### **2. Object Detection and Classification:** - **Image 1** includes a textual index with keywords and corresponding page numbers. #### **3. Scene and Activity Analysis:** - **Image 1** is a textual scene showing an index list for a document. It lists various keywords in alphabetical order (K, L, M, N, P, Q, R, S) with corresponding page numbers. This page forms part of an index section used for quickly locating specific topics within the document. #### **4. Text Analysis:** - **Image 1** contains text organized into two columns: 'Key word' and 'Page.' - Key points: - **Keywords:** Terms related to statistical and machine-related concepts like "Class width Δx", "Correction factor k", "Machine optimization", "Measuring method," etc. - **Page Numbers:** Indicating where to find these topics within the document, aiding navigation and quick reference. #### **5. Diagram and Chart Analysis:** - There are no diagrams or charts in **Image 1**. #### **6. Product Analysis:** - No products are depicted. #### **7. Anomaly Detection:** - There are no visible anomalies or unusual elements in **Image 1**. #### **8. Color Analysis:** - The page is predominantly black and white text. #### **9. Perspective and Composition:** - **Image 1** is a straightforward flat view of a textual document page. The text is well-aligned and organized into columns, making it easy to navigate. #### **10. Contextual Significance:** - **Image 1** serves as an index page in a document. Indexes are crucial for quickly locating information within lengthy documents, enhancing user experience and navigation. #### **12. Graph and Trend Analysis:** - No graphs are included in **Image 1**. #### **14. Ablaufprozesse (Process Flows):** - There are no specific process flows shown; the document references various topics and terms. #### **16. Typen Bezeichnung (Type Designations):** - **Image 1** includes type designations and classifications such as "normal distribution," "standard deviation σ," "quantile," etc., crucial for statistical references and studies. #### **14. Text and Table Analysis:** - **Image 1** comprises a table of contents-style format with categorized keywords and their respective page numbers. - **K:** e.g., "Class width Δx" - Page 17; "Correction factor k" - Page 17. - **M:** e.g., "Machine optimization" - Page 29; "Measuring method" - Page 24. - ...and so forth for the other letters. The keywords listed represent technical terms and concepts typically used in quality management, statistical analysis, and machine operation documentation. This detailed breakdown will aid in understanding the structure and purpose of the content within the provided page from the document. #################### File: VW%2010130_EN%281%29.pdf Page: 36 Context: # Key word | Keyword | Page | |--------------------------------------------|------| | Statistical percentage range | 18 | | Sampling | 24 | | Random sample range | 24 | | Dispersion range limits | 3, 10| | Swed-Eisenhard test | 20 | ## T | Term | Page | |-------------------------------------------|------| | Test - for outliers | 20, 26| | Test - for specified distribution model | 20, 26| | Test - for change of production location | 20, 26| | Tolerance expansion | 29 | | Tolerance zone | 3, 8 | | Toleranced characteristic | 4 | | Tolerance - on one side, upward | 9, 16| | Tolerance - on one side, downward | 9, 16| | Tolerance - on two sides | 9, 16| | Trend curve | 26 | ## V | Term | Page | |-------------------------------------------|------| | Variance σ² | 4 | | Distribution | 4 | | Distribution-free estimate | 16, 27| | Distribution function F(x) | 5 | | Distribution model | 4 | | Confidence range limit | 18 | | Premachining quality | 24 | ## W | Term | Page | |-------------------------------------------|------| | Probability p | 5 | | Probability density function f(x) | 4 | | Probability grid | 27 | | Weibull distribution | 8 | | Tooling change / adjustment | 24 | | w-Distribution | 17 | ## Z | Term | Page | |-------------------------------------------|------| | Random influences | 3 | Image Analysis: ### Text Analysis: **Image 1:** **Detected Text:** ``` Page 36 VW 101 30: 2005-02 Key word Page Statistical percentage range 18 Sampling 24 Random sample range 24 Dispersion range limits 3, 10 Swed-Eisenhard test 20 T Test - for outliers 20, 26 - for specified distribution model 20, 26 - for change of distribution location 20, 26 Tolerance expansion 29 Tolerance zone 3, 8 Toleranced characteristic 4 - on one side, upward 9, 16 - on one side, downward 9, 16 - on two sides 9, 16 Trend curve 26 V Variance σ Distribution Distribution-free estimate 16, 27 Distribution function f(x) 5 Distribution model 4 Confidence range limit 18 Premachining quality 24 W Probability p 5 Probability density function f(x) 4 Probability grid 27 Weibull distribution 8 Tooling change / adjustment 24 w-Distribution 17 Z Random influences 3 ``` **Analysis:** - The text is mainly a table of contents from section "Key word" to keywords starting with "Z". - This table of contents is designed to guide readers to specific sections and pages where defined terms or concepts are discussed within the document. - Each keyword is associated with a page number or numbers, indicating where the information can be found. - This structured layout suggests it is part of a manual, guide, or technical document, facilitating ease of navigation for the reader. ### Localization and Attribution: **Image 1:** - This image appears to be a single page, possibly from a larger document, identified at the top as "Page 36". ### Metadata Analysis: - No metadata is available from the image itself to provide further context or technical details about the capture conditions or date. ### Contextual Significance: - Given that the text is a table of contents/page index, it is crucial for navigating the document effectively. - The inclusion of page numbers suggests a well-organized document aimed at technical professionals who require quick access to specific sections. ### Perspective and Composition: **Image 1:** - The image is captured from a straight-on, eye-level perspective, making the text easy to read and uniformly aligned. - The layout is typical for a contents page, likely taken from a technical document or manual, suggesting an organized and methodical composition. ### Color Analysis: - The image is in black and white, which is typical for textual documents to maintain clarity and minimize distractions. - Dominant color: Black text on white background, providing high contrast for optimal readability. ### Diagram and Chart Analysis: - There are no diagrams or charts to analyze in this image. ### Object Detection and Classification: - The image consists purely of text, with no other objects detected. This comprehensive analysis covers all relevant aspects that can be derived from the provided image content. #################### File: Interni%20smernice%20-%20komponenty%20SZ_CZ.pdf Page: 1 Context: # Škoda Auto a.s. ## Směrnice pro sjednocení prvků **Projekt Obnova výrobních zařízení provozu PKG** **Datum vydání:** 28.01.2020 **PSZ/I - Metodika a standardizace** **1 - H - 20 CZ** Tato směrnice neruší platnost dříve vydaných směrnic, norem, požadavků zadání a ITS ŠkodaAuto. Pro komponenty, u kterých je povoleno několik dodavatelů, bude při zadání dodávky zařízení ve vztahu k projektu smluvně stanoven vždy jen jeden dodavatel. Potenciální dodavatelé jsou dodavatelé, kteří uvolnění pro projekt již mají, nebo je předpoklad, že po vykoušení a splnění koncernových standardů uvolnění do projektu mohou ještě dosat. ### Zpracoval: - Martin Janata, PSZ/I/12, tel.: +420 732 294 691 - Milan Výparnický, PKG/4, tel.: +420 732 294 226 ### Schválil: - Aleš Ivanovič, PSZ/I, tel.: +420 730 869 870 - Ing. Ladislav Treml, PKG/4, tel.: +420 732 294 945 - Ing. Roman Taneček, PPK/2, tel.: +420 604 292 729 ### Přehled změn: | Datum | Strana | Poznámky | |------------|------------------|-----------------------| | 28.01.2020 | První vydání | | **Podpisy, razítka** *Stránka 1 z 5* Image Analysis: ### Comprehensive Examination of the Attached Visual Content **Image 1 (Positioned centrally on the page):** --- **1. **Localization and Attribution:** - Single image located centrally on the page. - Numbered as Image 1. **2. **Object Detection and Classification:** - A document with text, tables, and several stamps. - Visible elements include Škoda Auto a.s. logo, text content, signatures, stamps, and a small table at the bottom. **3. **Text Analysis:** - **Header Text:** - “Škoda Auto a.s.” - “Směrnice pro sjednocení prvků” - “Projekt Obnova výrobních zařízení provozu PKG” - “PSZ/1 - Metodika a standardizace” - “Datum vydání: 28.01.2020” - **Main Body Text:** - Describes the guidelines for orders involving multiple suppliers and details regarding supplier selection for the project. - Contact information and responsible persons are provided. - **Table Content:** - A table with columns “Datum,” “Strana,” and “Poznámky.” - Entries include “28.01.2020” under Datum, “První vydání” under Poznámky, and an empty space under Strana. - **Signatures and Stamps:** - Includes names and signatures for approval, as well as various approval stamps indicating different departments and authorities. **6. **Product Analysis:** - No specific products depicted, but the overall document structure resembles official documentation for project guidelines, approvals, and standardizations. **9. **Perspective and Composition:** - Perspective: Direct front-facing view. - Composition: Standard document layout with a header, body text, contact details, signatures, stamps, and a table at the bottom. Elements are arranged logically and clearly for easy comprehension. **10. **Contextual Significance:** - The document seems to be an official guideline for the unification of project elements and standardization methodology at Škoda Auto a.s. - It is likely part of a larger report or collection of guidelines, as indicated by “Stránka 1 z 5” (Page 1 of 5). **11. **Metadata Analysis:** - The capture date is “28.01.2020.” - Contains official signatures and stamps indicating the document is authentic and reviewed by authorized personnel. **13. **Graph Numbers:** - The entry in the table: “28.01.2020” in Datum, and “První vydání” in Poznámky. --- ### Abbreviations and Acronyms Analyzed: - **PSZ/1**: Likely refers to a particular section or department in Škoda Auto. - **PKG**: Another department or section, possibly related to production. - **Telecommunication Numbers**: Provided for contact. --- In summary, this image contains an official Škoda Auto a.s. document detailing some standardization and methodological guidelines. The document is structured with clear headers, tabulated data, and necessary signatures for authentication. It appears to be a formal and critical piece of company documentation with procedural guidelines likely used in project management and supplier interaction at Škoda Auto a.s. #################### File: Interni%20smernice%20-%20komponenty%20SZ_CZ.pdf Page: 2 Context: # Škoda Auto a.s. **Směrnice pro sjednocení prvků** Projekt Obnova výrobních zařízení provozu PKG **Datum vydání:** 28.01.2020 **PSZ/1 - Metodika a standardizace** **1 - h - 20 CZ** ## I. Část: Standardy výrobních zařízení a komponentů Závazné jsou níže uvedené standardy v oblasti výroby agregátů koncernu VW: 1. Lastenhět Mechanik (dále jen KLH Mechanik) 2. Lastenhět Elektrik (dále jen KLH Elektrik) 3. ITS ŠkodaAuto, viz.: - [CZ verze](#) - [DE version](#) | **Poř.** | **Výrobní zařízení/komponenty** | **Uvolnění dodavatelé** | **Potenciální dodavatelé** | **Poznámky** | |----------|------------------------------------------------|---------------------------------|----------------------------|---------------------------------| | 1. | Elektrika | Viz. část elektro, str.3-4 | ITS: 1.11, 5.13 | | 0.1 | Dokumentace elektrika a řídící technika | Eplan P8 ver. 2.2 nebo vyšší | | | | 2. | Mechanika | Festo, SMC | ITS: 1.10 | | 3. | Pneumatika | Norgren | ITS: 1.13 | | 4. | Mazání | SKF Lubrikation | ITS: 1.17 | | 5. | Hydraulika | Bosch Rexroth, Parker | ITS: 1.12 | | 6. | Filtrační technika | Hydac, Mahle, Bosch Rexroth | ITS: 1.12 | | 0.6 | Čerpadla | KSB, Knoll, Grundfos | Viz KLH Mechanik | | 7. | Šroubová technika | Bosch Rexroth | Bosch Rexroth systém BS350 | ## II. Část: Elektrika, řídicí systémy Image Analysis: ### Detailed Analysis of the Attached Visual Content #### 1. **Localization and Attribution:** **Image Position:** The image is taken from a document, likely a PDF, and is positioned as a standalone page. #### 2. **Object Detection and Classification:** - **Objects Detected:** - Company Logo of Škoda Auto. - Text blocks and headings. - Table containing data on manufacturing standards and suppliers. - Hyperlinks (CZ verze, DE version). **Categories:** - Corporate branding (logos, headers) - Text content (document text) - Tabular data (industrial standards and suppliers) #### 3. **Scene and Activity Analysis:** The image appears to be a page from a professional document related to manufacturing standards for a project by Škoda Auto. It focuses on the methods and standardizations of manufacturing processes, specifically for the machinery and electrical components used in production. #### 4. **Text Analysis:** **Text Extracted:** - Document title and date issued: "Škoda Auto a.s., PSZ/1 - Metodika a standardizace, Datum vydání: 28.01.2020." - Section headers: "I. Část: Standardy výrobních zařízení a komponentů" - Important points: 1. Lastenheft Mechanik 2. Lastenheft Elektrik 3. ITS ŠkodaAuto - Table with standards and suppliers, including: - Elektrika, Mechanika, Pneumatika, Hydraulika, Filtrační technika, etc. - Relevant standards, suppliers, and notes. **Significance:** This text outlines the components and standards required for the production processes at Škoda Auto, listing approved suppliers and potential alternative suppliers. The inclusion of hyperlinks suggests available versions of the standards in Czech and German. #### 5. **Diagram and Chart Analysis:** The table presented is an essential tool. It highlights the necessary standards and component suppliers for the project. Key columns include: - **Výrobní zařízení/komponenty:** Types of components or devices involved. - **Uvolnění dodavatele:** Approved suppliers. - **Potenciální dodavatelé:** Potential suppliers. - **Poznámky:** Notes or additional comments. #### 7. **Anomaly Detection:** There are no obvious anomalies in the document. It is structured and formatted logically according to professional standards. #### 8. **Color Analysis:** The dominant colors in the document are black text on a white background, with a distinctive green color used in the table for headers. The green is likely to highlight important sections, drawing attention to the key areas. Yellow is used for highlighting the 'Poznámky' (Notes) column. #### 9. **Perspective and Composition:** The image is a scan or screenshot of a document page, viewed from a straight-on perspective, providing a clear and direct view of the text and table. The composition is balanced, with the logo and headers at the top and the table centered. #### 10. **Contextual Significance:** This page likely forms part of a larger manual or guideline document (as indicated by "Stránka 2 z 5"), which sets the standards for Škoda Auto’s manufacturing processes. The detailed listing of components and suppliers suggests its use as a technical and operational reference. ### **Conclusion:** This image is from a detailed technical document used by Škoda Auto to standardize and outline the necessary manufacturing components and approved suppliers. It forms part of their methodological and standardized approach to production, with a clear and concise table listing essential standards and notes. #################### File: Interni%20smernice%20-%20komponenty%20SZ_CZ.pdf Page: 3 Context: # Škoda Auto a.s. **PSZ/21 - Metodika a standardizace** **Datum vydání:** 28.01.2020 | Poř. | Výrobní zařízení/komponenty | Uvolnění dodavatelé | Potenciální dodavatelé | Poznámky | |------|----------------------------------------------------|-----------------------------------------|------------------------------------------|-------------------------------| | 1 | Řídicí systém SPS(PLC) | Siemens | Siemens Simatic S7 řada 1500 - TIA V14 a vyšší | | | 2 | CNC Řízení | Siemens | Siemens (Sinumeric 840D sl.) | | | 3 | Řídicí systém na bázi PC a panelové PC | Siemens | Systém - Simatic S7 (HW SPS) Profinet | | | 4 | Vizualizace | Siemens WinCC Flexible | WinCC Flexible 2008 | | | 5 | Ovládací panely | Siemens | | | | 6 | Decentrální sběrnice | Profinet | Profibus, IO-link | | | 6.1 | Konektorové pasivní slučovače (snímače,ventily) | Balluff, Murrelektronik | Balluff, IO-link | | | 7 | Decentrální periferie | Siemens | | | | 8 | Robot | ABB | Kuka (Kuka s řízením VRKC 4) | Turck BL67 | | 9 | Elektrické frekvenční pohony - měniče | SEW Eurodrive | Siemens | VW Konzern Freigabe | | 10 | Elektrické servo pohony | Siemens, Bosch Rexroth | Siemens | VW Konzern Freigabe | | 11 | Ovládací prvky - tlačítka, kontroly | Schneider Electric | Schneider Electric | Specifikace Škoda Auto a.s. | | 12 | Dvouručný ovladač | Schneider Electric | Schmersal-Elan | Specifikace Škoda Auto a.s. | | 13 | Elektro skrín | Rittal | Rittal | VW Konzern Freigabe | | 14 | Svrchní skříň | Rittal | Plannenberg | VW Konzern Freigabe | | 15 | Chalzení rozvádzačových skříní (klimatizace) | Rittal | Sick | Specifikace Škoda Auto a.s. | | 16 | Svételení zovránící/scanner | ASO - Contra, Pilz, Schneider Electric | Cognex, Keyence, Balluff | Specifikace Škoda Auto a.s. | | 17 | Čtecí zařízení čárového a DMC kódu | IOSS | Balluff, Turck-Banner | Specifikace Škoda Auto a.s. | | 18 | Identifikační systém a jistič prýky | Schneider Electric | Pepperl+Fuchs, Turck-Banner | Specifikace Škoda Auto a.s. | | 19 | Optický senzor | Sick, IFM Electronic, Balluff | | | Image Analysis: ### Localization and Attribution **Context:** - The image appears to be a document page from Škoda Auto a.s. - The document is titled "PSZ/1 - Metodika a standardizace" and relates to "Projekt Obnova výrobních zařízení provozu PKG". - The document is dated 28.01.2020 and is labeled as "1 - H - 20 CZ". ### Scene and Activity Analysis - The scene shows a structured table detailing manufacturing or industrial equipment/components. - Each row identifies a specific type of equipment along with associated columns indicating different manufacturers, potential suppliers, and notes. ### Text Analysis - **Header and Title:** - "Škoda Auto a.s." - "PSZ/1 - Metodika a standardizace" - "Projekt Obnova výrobních zařízení provozu PKG" - "Datum vydání: 28.01.2020" - "1 - H - 20 CZ" - "Stránka 3 z 5" (Page 3 of 5) - **Table Headers:** - "Poř." (No.) - "Výrobní zařízení/komponenty" (Manufacturing Equipment/Component) - "Uvolnění dodavatele" (Approved Suppliers) - "Potencionální dodavatelé" (Potential Suppliers) - "Poznámky" (Notes) - **Table Contents:** - Enumerates 20 various pieces of manufacturing or control equipment, listing suppliers and notes for each. - Each row lists manufacturers, potential suppliers, and relevant notes. For example: - "Řídicí systémy SPS/PLC" (Control Systems SPS/PLC) - Siemens - Notes: "Siemens Simatic S7 řada 1500 - TIA V14 a výšší". - "CNC Řízení" (CNC Control) - Siemens - Notes: "Siemens (Sinumerik 840D sl.)". ### Color Analysis - The color scheme comprises mainly white, black text, and a light green highlight for certain rows, primarily spanning suppliers and potential suppliers columns. - The use of green highlights certain aspects, enhancing readability and making it easier to differentiate sections. ### Diagram and Chart Analysis - No diagrams or charts are presented in the image. ### Product Analysis - **Types of Equipment Listed:** - Control systems (SPS/PLC, CNC Control) - Visual systems (Siemens WinCC Flexible) - Robots (e.g., ABB) - Electrical drives and controls - Safety and protection equipment - **Main Features:** - Emphasis on systems and controls primarily from Siemens, with alternative manufacturers and models mentioned. - Notes column often specifies versions or features, e.g., "Sistema Simatic S7" or "WinCC Flexible 2008". ### Tables - The table efficiently organizes different types of industrial equipment, providing clear information on approved and potential suppliers along with additional notes. - It is structured in a way that prioritizes quick reference and decision-making facilitated by the notes. ### Perspective and Composition - The image is a direct, high-angle view, providing a clean, readable presentation of the table. - The information is neatly ordered and segmented, making it easy to navigate section by section. ### Contextual Significance - This document appears to be part of a larger document set (page 3 of 5). - The organization and type of information suggest it’s meant for stakeholders involved in the procurement or standardization process within Škoda Auto’s manufacturing operations. ### Anomaly Detection - No anomalies are detectable in this structured document. The design and layout are standard for industrial documentation. ### Summary The image is a well-structured and standardized industrial document from Škoda Auto detailing manufacturing equipment and components. It emphasizes control systems, various types of equipment, their approved and potential suppliers, and related notes. The document uses a clear table format with color highlights to enhance readability and facilitate efficient decision-making in procurement or standardization processes. #################### File: Interni%20smernice%20-%20komponenty%20SZ_CZ.pdf Page: 4 Context: # Škoda Auto a.s. **Směrnice pro sjednocení prvků** **Projekt Obnova výrobních zařízení provozu PKG** **Datum vydán: 28.01.2020** **1 - H - 20 CZ** | Poř. | Výrobní zařízení/komponenty | Uvolněný dodavatelé | Potenciální dodavatelé | Poznámky | |------|----------------------------------------------------|-------------------------------------------|------------------------------------------|--------------------------------------| | 21 | Indukční senzory, polohové spínače a koncové spínače | Balluff, IFM Electronic | Sick | Specifikace Škoda Auto a.s. | | 22 | Svorky a svorkové příslušenství | Phoenix Contact, Wago | Siemens | Specifikace Škoda Auto a.s. | | 23 | Průtokoměry a teploměry | IFM Electronic, Hydac | Parker, Bosch Rexroth | Specifikace Škoda Auto a.s. | | 24 | Instalace senzorů a koncových spínačů | Balluff - Lumberg | Pepperl+Fuchs | Specifikace Škoda Auto a.s. | | | kabely, konektory a příslušenství snímačů | Mur elektronki | | | | 25 | Konektory - těžké a lehké | Harting, Phoenix Contact, Weidmüller | Murrelektronik | | | 26 | Světelná signalizace - majáky a signální světla | Murrelektronik | Siemens | | | 27 | Výsoké bezpečnostní spínače | Schmersal | Balluff | | | 28 | Bezpečnostní spínače - ochranných zařízení, okén, atd. | Pilz, Schmersal | Euchner | | | 29 | Bezpečnostní systém a bezp. moduly | Pilz, Siemens | Schneider Electric | Pilz (PNOZsigma) | | 30 | Mechanické koncové spínače | Balluff, Siemens | Euchner | Specifikace Škoda Auto a.s. | | 31 | Instalční kabely | LAPP Kabel | Hellu kabel | | | 32 | Vysoké flexibilní kabely | LAPP Kabel | Hellu kabel | | | 33 | Přepínací obvody | Hakel | ABB | | | 34 | Kabelové kanály a žlaby | OBO-Betterman, Niedax | Kopos Kolin | | | 35 | Energetické případy kabelové trasy | Murphysit, Brevett | Kableschlepp | | | 36 | Optické snímače | IFM, Keyence | Sick | Specifikace Škoda Auto a.s. | | 37 | Kamejnzové svítilny, údržba | Cognex, Keyence, Sick | Specifikace Škoda Auto a.s. | | 38 | HEIDENHAIN | | | | **Stránka 4 z 5** Image Analysis: **Text Analysis:** 1. **Primary Header:** - Text: "Škoda Auto a.s." - Context: Indicates the branding of the document, relating to Škoda Auto. 2. **Sub-headers:** - Text: "PSZ/1 - Metodika a standardizace" and "Směrnice pro sjednocení prvků Projekt Obnova výrobních zařízení provozu PKG" - Context: Details the methodology and standardization for an element unification project for the renovation of production facilities in PKG. 3. **Date Information:** - Text: "Datum vydání: 28.01.2020" - Context: Shows the issue date of the document, important for version control and relevance. 4. **Column Headers and Table Content:** - Column 1: "Poř." - Item number in the list, providing a sequence. - Column 2: "Výrobní zařízení/komponenty" - Manufacturing equipment/components, listing various technical items. - Column 3: "Uvolnění dodavatelé" - Released suppliers, listing approved suppliers for each item. - Column 4: "Potenciální dodavatelé" - Potential suppliers, listing additional suppliers that could be considered. - Column 5: "Poznámky" - Notes, providing additional information or specifications for each item. 5. **Rows from 21 to 38:** - The table includes specific components such as "Indukční senzory, polohové spínače a koncové spínače" (Inductive sensors, position switches, and limit switches). - Indicates approved suppliers like "Balluff, IFM Electronic" and potential suppliers like "Sick." - Notes specify adherence to "Specificace Škoda Auto a.s." for many items, ensuring they meet Škoda's standards. **Structure and Layout Analysis:** 1. **Document Layout:** - The visual content is organized as a structured table spanning rows 21 to 38, with clear column headers and slight coloring for rows to enhance readability. 2. **Branding and Design:** - Contains the Škoda logo, reinforcing the brand. - Consistent use of fonts and colors within the table for professional appearance. **Table Analysis:** 1. **Contents Overview:** - Lists various industrial components and equipment essential for manufacturing. - Specifies suppliers both currently approved ("Uvolnění dodavatelé") and potential options ("Potenciální dodavatelé"). 2. **Detailed Data:** - Each row provides comprehensive details about a specific component, emphasizing compatibility and standards specific to Škoda Auto. - Notes offer insightful commentary enabling quick understanding of compliance requirements. **Anomaly Detection:** - **Uniformity and Structure:** - No evident anomalies; the table follows a consistent structure and presents data clearly. **Color Analysis:** - **Dominant Colors:** - Predominantly white background with black text for readability. - Light yellow and gray shades highlight alternate rows, aiding in differentiating between lines. **Conclusion:** The provided visual content is a well-organized table from Škoda Auto detailing component suppliers and specifications. It primarily serves as a reference for standardizing equipment and components in their manufacturing processes. #################### File: Interni%20smernice%20-%20komponenty%20SZ_CZ.pdf Page: 5 Context: # Škoda Auto a.s. **Směrnice pro sjednocení prvků** **Projekt Obnova výrobních zařízení provozu PKG** **Datum vydání:** 28.01.2020 | PSZ/1 - Metodika a standardizace | 1 - H - 20 CZ | |-----------------------------------|---------------| | 39. Záložní zdroje napájení | Siemens, APC, Murrelektronik | Phoenix Contact | | 40. Tlakové snímače | Rexroth, Parker, IFM | Hydac | | | | Specifikace Škoda Auto a.s. | **Stránka 5 z 5** Image Analysis: ### Localization and Attribution 1. **Localization and Attribution:** - There is only one image located on the page. - This image will be referred to as **Image 1**. ### Object Detection and Classification 2. **Object Detection and Classification:** - The image contains a table embedded within a document. - Key features include text rows, columns, logos, and boxed sections. ### Text Analysis 4. **Text Analysis:** - **Title:** "Škoda Auto a.s." - **Sub-Title:** "PSZ/1 - Metodika a standardizace" - **Additional Text:** - "Směrnice pro sjednocení prvků" - "Projekt Obnova výrobních zařízení provozu PKG" - **Date:** "Datum vydání: 28.01.2020" - **Table Content:** - **Header:** "1 - H - 20 CZ" - **Row 1:** - Column 1: "39. Záložní zdroje napájení" - Column 2: "Siemens, APC, Murrelektronik" - Column 3: "Phoenix Contact" - **Row 2:** - Column 1: "40. Tlakové snímače" - Column 2: "Rexroth, Parker, IFM" - Column 3: "Hydac" - **Additional Note:** "Specifikace Škoda Auto a.s." ### Color and Composition Analysis 8. **Color Analysis:** - The dominant colors are white and black with teal (a shade of green) used in the logo and the header. - The simplicity of the color scheme lends itself to a clean and professional look, suitable for official corporate documentation. 9. **Perspective and Composition:** - The image is a head-on view of the document, captured from a standard 'document scan' perspective. - The composition is structured with clear horizontal and vertical delineations defining the sections and rows of the table. ### Contextual Significance 10. **Contextual Significance:** - This document appears to be a technical specification or directive for standardized procedures and components related to Škoda Auto a.s. - It suggests a focus on unifying parts and procedures within the company’s operations, likely aimed at consistency and efficiency in production. ### Tables 13. **Tables:** - The table outlines specific components and their respective suppliers for two different categories: - **Row 1 (Záložní zdroje napájení):** Siemens, APC, Murrelektronik with Phoenix Contact as an additional note. - **Row 2 (Tlakové snímače):** Rexroth, Parker, IFM with Hydac as an additional note. ### Key Insights - The document is likely a page out of a technical or procedural manual from Škoda Auto a.s. focused on guiding the standardization of various components used within their operations. The table lists essential components and their recommended suppliers, providing specific information crucial for maintaining uniformity in production. The detailed breakdown into categories and specific supplier lists indicates a well-organized approach to procurement and standardization. This analysis covers the requested aspects: localization, object detection, text analysis, color analysis, perspective and composition, contextual significance, and the tables provided in the document. #################### File: VW%2010130_DE%281%29.pdf Page: 2 Context: # Einleitung Eine Bewertung der Maschinenfähigkeit bezüglich betrachtbarer messbarer Fertigungsmerkmale ist eine wichtige Voraussetzung zur Erfüllung der festgelegten Qualitätsforderungen. Für viele Praxisfälle der Fähigkeitsuntersuchung gab es jedoch bis dahin keine normativen oder einheitlichen Konzeptionen, sodass in gleichen Fällen völlig unterschiedliche Fähigkeitsbewertungen ergeben konnten. Um die Fähigkeitsuntersuchung nach einheitlichen Regeln für alle Praxisfälle durchzuführen und damit die Vergleichbarkeit der Ergebnisse im VW-Konzern sicherzustellen, wurde daher diese Norm erarbeitet. Die Norm enthält in geschlossenem Text vollständig die theoretischen Grundlagen, die zur Anwendung und zum Verständnis erforderlich sind. Lediglich die statistischen Tests, die bereits in Normen oder Standardwerken der Statistikliteratur ausführlich beschrieben sind, werden nur mit Verweisen angegeben. Zur Durchführung einer Maschinenfähigkeitsuntersuchung nach dieser Norm ist ein EDV-Programm erforderlich, in dem die beschriebenen Algorithmen umgesetzt sind. Steht ein solches EDV-Programm zur Verfügung, so kann sich der Anwender im Wesentlichen auf die in Abschnitt 4 beschriebenen Regelungen beschränken und hat Bedarf theoretische Grundlagen nachzulesen. Die wichtigsten Unterabschnitte darin sind wiederum: - 4.2 Stichprobenahme - 4.5 Dokumentation - 4.6 Ergebnisbeurteilung Im Abschnitt 5 sind zudem Beispiele aufgeführt, die als Hilfe zur Ergebnisbeurteilung dienen sollen. ## 1 Zweck und Anwendungsbereich Ziel einer Maschinenfähigkeitsuntersuchung ist eine dokumentierte Bewertung, ob die zu untersuchende Maschine eine sichere Fertigung eines betrachteten Merkmals innerhalb definierter Grenzwerte ermöglicht. Idealerweise sollen dabei nur machinebedingte Einflüsse auf den Fertigungsprozess zur Wirkung kommen. Wie und unter welchen Voraussetzungen Maschinenfähigkeitsuntersuchungen durchzuführen sind, ist Gegenstand dieser Norm. Sie ist anwendbar auf beliebige kontinuierliche (messbare) Fertigungsmerkmale. Image Analysis: ### Image Analysis #### Localization and Attribution 1. **Image Position:** - There is a single image present, and it is labeled as **Image 1**. #### Text Analysis 1. **Text Content:** - Title: "VW 101 30: 2005-02" - Sections: - **Introduction:** - Discussion about the importance of evaluating machine capabilities concerning measurable production features to fulfill quality requirements. - The need to ensure comparability of results across VW companies by following unified rules for practical cases. - The norm contains theoretical foundations and procedures for carrying out machine capability evaluations. - Specific Sections: Sampling (4.2), Documentation (4.5), and Results Evaluation (4.6). - **Purpose and Application Area:** - Aim: Documented evaluation to ensure that a machine can produce within defined limits for observed features. - Emphasis on machine-induced effects and process conditions. - Applicability: Any continuous measurable production features. - Footnote: - Clarification on terminology usage, stating that "measurable features" are used according to VW standards, instead of the DIN recommended "continuous features". 2. **Analysis and Significance:** - The document appears to discuss a standardized method for evaluating machine capability within VW companies. - It emphasizes the importance of clear, consistent measurements and documentation to ensure production quality. - The sections mentioned (Sampling, Documentation, Results Evaluation) suggest a structured approach to capability evaluation. #### Language Analysis: - The text is written in German and addresses technical and procedural guidelines for evaluating machine capabilities. ### Contextual Significance 1. **Context and Contribution:** - The image seems to be a part of a technical manual or standard document for Volkswagen (VW). - It provides foundational information laying out the importance, procedures, and application guidelines for machine capability assessments. - Its contribution to the overall document or website would be foundational, ensuring that readers understand the purpose and methods of evaluation right from the onset. ### Conclusion This single image provides a detailed introduction to the criteria and methods for assessing machine capabilities within VW companies, emphasizing the significance of standardized procedures for quality assurance in production processes. The text is methodical and likely part of a larger document detailing comprehensive procedures for these evaluations. #################### File: VW%2010130_DE%281%29.pdf Page: 3 Context: # 2 Prinzip der Maschinenfähigkeitsuntersuchung Aufgrund von Zufallseinflüssen ergeben sich bei der Fertigung von ähnlichen Teilen mit der untersuchten Maschine grundsätzlich unterschiedliche Werte eines betrachteten Merkmals. Diese Merkmalswerte\* streuen in nach Fertigungsqualität ein von systematischen Einflüssen bedingte Lage. Es wird daher untersucht, wie die Verteilung der Merkmalswerte in eine konstruktiver definierte Toleranzintervalle passt (Bild 1). Die Bewertung dazu wird durch die Fähigkeitskennwerte \(C_{pk}\) und \(C_{mk}\) (von capability) ausgedrückt, wobei durch den \(C_{pk}\)-Wert nur die Fertigungsstreuung und durch den \(C_{mk}\)-Wert auch die Fertigungslage berücksichtigt wird. Diese Kenntnisse müssen mindestens so groß wie definierte Grenzwerte sein, um die Forderung nach einer fähigen Maschine zu erfüllen. Zur Ermittlung der Fähigkeitskennwerte bezüglich des betrachteten Merkmals wird eine genügend große Stichprobe (in der Regel n = 50) gefertigter Teile in direkter Folge unter möglichst idealen Bedingungen der Einflusskategorie Material, Mensch, Methode und Umwelt entnommen, um wesentliche nur den Maschineneinfluss zu erfassen. Aus dieser Stichprobe werden Lage \(μ\) und Streubreiten \(X_{0,135}\) und \(X_{0,865}\) für die Grundsamtheit der Merkmalswerte (theoretisch unähnliche Anzahl) erwartungstreu geschätzt und mit dem Toleranzintervall \([G_L, G_U]\) verglichen (Bild 1). Die Streubreiten werden dabei so festgelegt, dass der Anteil von Merkmalswerten außerhalb des Streubereichs zu beiden Seiten jeweils \(p_L = 0,135\%\) beträgt. Zudem wird überprüft, ob die Verteilung der Merkmalswerte einer erwarteten Gesetzmäßigkeit entspricht. ## Toleranz ### Bild 1 - Beispiel einer Verteilung von Merkmalswerten innerhalb eines definierten Toleranzintervalls \[ p_L = 0,135\% \] \[ p_U = 0,135\% \] \[ G_L = 0,135\% \] \[ μ \] \[ X_{0,865} \text{ und } G_U = 99,865\% \] \* Der Begriff Merkmalswert ist nicht zu verwechseln mit dem Begriff Messwert, da letzterer gegenüber ersteren eine Unsicherheit enthält. Zur Bezeichnung der Grenzwerte ist auch USG, OSG oder USL, OSL oder TL zuzulässig. Image Analysis: ## Comprehensive Analysis of the Image ### 1. Localization and Attribution - **Image Placement:** The document contains a single page with one chart/diagram at the bottom. - **Numbering of Images:** - Image 1: Entire document page including the diagram ### 2. Object Detection and Classification - **Image 1:** - **Objects Detected:** - Text blocks: The majority of the page is occupied by a text block. - Chart/Diagram: A graph with accompanying labels and legends. - **Key Features:** - The document appears to be a technical or instructional page. - The diagram is positioned below the main textual content. ### 3. Scene and Activity Analysis - **Image 1:** - **Scene Description:** The scene depicts a technical document page focusing on machine capability investigation or "Maschinenfähigkeitsuntersuchung." - **Activities:** The document describes the principles and procedures for assessing machine capability with the assistance of a chart explaining the distribution of characteristic values within a defined tolerance interval. ### 4. Text Analysis - **Image 1:** - **Text Extracted:** - **Main Heading:** "Prinzip der Maschinenfähigkeitsuntersuchung" - **Text Content:** - The main body discusses factors influencing machine capability, the concept of manufacturing variability, and how this affects the quality of produced parts. - A figure label: "Bild 1 - Beispiel einer Verteilung von Merkmalswerten innerhalb eines definierten Toleranzintervalls," which translates to "Figure 1 - Example of a distribution of characteristic values within a defined tolerance interval." - Detailed explanations of constraints and machine capability indicators. - **Significance:** The text introduces theoretical and practical aspects of machine capability analysis and provides explanations on how to interpret the data in the chart. ### 5. Diagram and Chart Analysis - **Image 1:** - **Diagram Placement:** Located at the bottom of the page. - **Data and Trends:** - The chart illustrates a normal distribution curve representing characteristic values within tolerance limits \(G_L\) and \(G_O\). - Key data points include values at \(p_{L} = 0.135\%\) for the left tail and \(p_{O} = 0.135\%\) for the right tail, highlighting specific tolerance margins. - **Axes, Scales, and Legends:** - The x-axis is labeled "Merkmalswert" (Characteristic Value). - The y-axis is labeled "Häufigkeit" (Frequency). - The chart shows the "definierte Prozessstreubreite" (defined process spread width) and labels the mean values \(\mu\). - **Key Insights:** This diagram provides a visual representation of how characteristic values are distributed within the tolerance interval and emphasizes the importance of controlling variability to maintain quality. ### 8. Color Analysis - **Image 1:** - **Color Composition:** Primarily black-and-white, typical for technical documents. - **Dominant Colors:** Black text and lines on a white background. - **Impact on Perception:** The monochromatic color scheme underscores the technical nature of the document and facilitates clear readability and comprehension. ### 9. Perspective and Composition - **Image 1:** - **Perspective:** The image is a front-facing view of a page from a technical document. - **Composition:** - The text occupies the upper two-thirds of the page. - The diagram is centrally located at the bottom, framed by the surrounding text. - This layout helps in a structured flow of information from theoretical explanations to practical illustration (diagram). ### 10. Contextual Significance - **Image 1:** - **Document Context:** The document appears to be an excerpt from a technical manual or educational material about machine capability testing. - **Contribution to Overall Message:** The image emphasizes the importance of understanding and controlling process variation to ensure manufacturing quality. It contributes to the overall educational intent of the document by combining theoretical descriptions with a visual tool for better understanding. ### 12. Graph and Trend Analysis - **Image 1:** - **Trend Analysis:** The diagram illustrates the normal distribution of characteristic values and highlights the deviation from the mean within the tolerance limits. - **Interpretation Significance:** Such a distribution is crucial for understanding process capability and quality control, showing how well a process can produce outputs within specified limits. ### 13. Graph Numbers - **Image 1:** - **Data Points:** - \(G_L (X_{0.135\%})\) on the left side indicating the lower specification limit. - \(\mu\) indicating the mean value. - \(G_O (X_{99.865\%})\) on the right side indicating the upper specification limit. - \(p_{L} = 0.135\%\) and \(p_{O} = 0.135\%\) ### Ablaufprozesse (Process Flows) - **Image 1:** - **Described Process Flows:** The document describes the process flow of evaluating machine capability by investigating characteristic value distribution within tolerance limits. ### Prozessbeschreibungen (Process Descriptions) - **Image 1:** - **Detailed Descriptions:** Detailed steps and considerations for conducting machine capability studies, addressing influences of material, environmental conditions, and inherent process variability. ### Typen Bezeichnung (Type Designations) - **Image 1:** - **Specified Types/Categories:** "Fähigkeitskennwerte" (capability indices) including \(C_{mk}\) are discussed as measures for machine capability. #################### File: VW%2010130_DE%281%29.pdf Page: 3 Context: ### Trend and Interpretation - **Image 1:** - **Trends:** The focus on maintaining high capability indices to ensure quality production. - **Interpretations:** Reinforces the need for precise control and monitoring in manufacturing processes. ### Tables (Included Internally) - **Image 1:** - **Analyzed Elements:** - Not applicable as there are no separate tables outside of the chart/diagram analyzed. This comprehensive analysis covers the various aspects of the image while highlighting the important technical elements provided in the document. #################### File: VW%2010130_DE%281%29.pdf Page: 4 Context: # 3 Theoretische Grundlagen ## 3.1 Verteilungsmodelle Die Verteilung von Merkmalwerten lässt sich für die meisten Arten von Fertigungsmerkmalen durch ein Verteilungsmodell beschreiben. So lässt sich für die meisten zweigleisig tolerierten Fertigungsmerkmale, z.B. Längenmaße, Durchmesser und Drehmomente, eine Normalverteilung zugrunde legen. Das Streuverhalten einseitig nach oben tolerierter Fertigungsmerkmale lässt sich dagegen in der Regel durch Betragsverteilungen der 1. oder 2. Art beschreiben. So lässt sich z.B. die Betragsverteilung 1. Art für die Merkmalsarten Parallelität, Asymmetrie und die Betragsverteilung 2. Art für die Merkmalsarten Position, Koaxialität zugrunde legen. ### 3.1.1 Normalverteilung Die Funktion der Wahrscheinlichkeitstichte (kurz Dichtefunktion) einer Normalverteilung, die grafisch in Bild 2 dargestellt ist, lautet: $$ f_X(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}} $$ mit den Parametern Mittelwert \(\mu\) und Standardabweichung \(\sigma\), die Lage und Breite einer Verteilung kennzeichnen, wobei das Quadrat der Standardabweichung \(\sigma^2\) als Varianz bezeichnet wird. ![Bild 2 - Funktion der Wahrscheinlichkeitstichte einer Normalverteilung](link-zum-bild) - **Merkmalswert** - \( \mu - 4\sigma \) - \( \mu - 3\sigma \) - \( \mu - 2\sigma \) - \( \mu - \sigma \) - \( \mu \) - \( \mu + \sigma \) - \( \mu + 2\sigma \) - \( \mu + 3\sigma \) - \( \mu + 4\sigma \) - **Wendepunkte** - \( p_e = 0.135 \) - \( p_e = 0.135 \) Image Analysis: ### Comprehensive Examination #### 1. Localization and Attribution: - **Image 1**: Located in the lower half of the page. #### 2. Object Detection and Classification: - **Image 1**: - Contains a graphical representation (line graph). - The graph is accompanied by annotations and a textual legend. #### 3. Scene and Activity Analysis: - **Image 1**: - The scene depicts a standard bell curve graph illustrating the probability density function of a normal distribution. - Key activities: Visualization of mathematical concepts related to the normal distribution. #### 4. Text Analysis: - **Page Text**: - Contains explanations about distribution models, specifically normal distribution. - Key terms identified: "Verteilungsmodelle", "Normalverteilung", "Wahrscheinlichkeitsdichte", "Mittelwert", "Standardabweichung", "Varianz", and others. - Equations: \[ f_{\text{N}}(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \] - The significance of the text lies in explaining the concept of the normal distribution, its properties, and its mathematical formulation. #### 5. Diagram and Chart Analysis: - **Image 1** (Graph Analysis): - Axes: - X-axis: Labeled "Merkmalswert" (Characteristic value), showing intervals such as \( \mu-4\sigma \), \( \mu-3\sigma \), up to \( \mu+4\sigma \). - Y-axis: Labeled "Wahrscheinlichkeitsdichte" (Probability density). - Graph Type: Bell curve representing the normal distribution. - Key features include: - Peak at \(\mu\) (mean). - Points marked at one standard deviation (\(\sigma\)) intervals. - Probability value (\(p\)) of 0.135% indicated at the tails (\( \mu-3\sigma\) and \(\mu+3\sigma\)). - Labels for significant points like "Wendepunkte" (inflection points). #### 7. Anomaly Detection: - **Image 1**: - There are no noticeable anomalies; the elements are consistent with a typical normal distribution curve. #### 8. Color Analysis: - **Image 1**: - Predominantly uses black, white, and variations of grey. - The monochromatic color scheme aids in clarity and focuses on the data without color distraction. #### 9. Perspective and Composition: - **Image 1**: - The perspective is a standard 2D view. - The composition is central, with the graph centered horizontally and balanced vertically, ensuring clear visibility of all annotations. #### 10. Contextual Significance: - **Image 1**: - The image serves as a visual aid to the surrounding textual explanation of normal distribution. - It supports the theoretical content by providing a tangible example of the probability density function. #### 13. Graph Numbers: - **Image 1**: - Data points are not numerically explicit but indicated through standard deviation markers and probability annotations. - Equally spaced intervals with significant points labeled relative to the mean (\(\mu\)) and standard deviations (\(\sigma\)). #### Additional Aspects: - **Ablaufprozesse (Process Flows)**: - Not directly depicted. - **Prozessbeschreibungen (Process Descriptions)**: - Detailed explanation of how normal distributions function and their key parameters. - **Typen Bezeichnung (Type Designations)**: - Types of distribution: Explained as Normalverteilung (Normal Distribution). - **Trend and Interpretation**: - Emphasizes the symmetric property and tails of the normal distribution. ### Summary The attached content is a detailed extension on the concept of normal distribution within statistical models. It explains theoretical foundations, mathematical formulations, and includes a significant diagram to visualize the normal distribution's probability density function. The image and accompanying text synergize to elaborate on statistical concepts crucial for understanding distribution models in a comprehensive manner. #################### File: VW%2010130_DE%281%29.pdf Page: 5 Context: ```markdown Als Wahrscheinlichkeit lässt sich in Bild 2 der Flächenanteil unterhalb des Grafen innerhalb eines betrachteten Intervalls interpretieren. Die Wahrscheinlichkeit, einen Merkmalswert x in einer Grundgesamtheit vorzufinden, der höchsten so groß wie ein betrachteter Grenzwert x ist, wird somit durch die Integralfunktion, die Verteilungsfunktion, angegeben. Diese lautet für die Normalverteilung: \[ F_V(x) = \int_{-\infty}^{x} f_V(t) \, dt \] (1.2) wobei \[ \int_{-\infty}^{x} f_V(x) \, dx = 1 \] (1.3) und \( f_V(x) \geq 0 \) für alle Werte x gilt. Mit der Transformation \[ u = \frac{x - \mu}{\sigma} \] (1.4) ergibt sich aus (1.1) die Wahrscheinlichkeitsdichte der standardisierten Normalverteilung \[ \varphi(u) = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}u^2} \] (1.5) und die Verteilungsfunktion \[ \Phi(u) = \int_{-\infty}^{u} \varphi(t) \, dt \] (1.6) mit der Standardabweichung \( \sigma = 1 \). ### 3.1.2 Betragverteilung 1. Art Die Betragverteilung 1. Art entsteht durch Faltung der Dichtefunktion einer Normalverteilung am Nullpunkt, wobei die Funktionswerte links vom Faltungsunkt zu denen rechts davon addiert werden. Die Dichtefunktion und die Verteilungsfunktion der Betragverteilung 1. Art lauten somit: \[ f_{A}(x) = \frac{1}{\sigma_N \sqrt{2\pi}} \left( e^{-\frac{(x - \mu_N)^2}{2\sigma_N^2}} \right) \text{ für } x \geq 0 \] (1.7) \[ F_{B}(x) = \Phi\left( \frac{x - \mu_N}{\sigma_N} \right) + \Phi\left( \frac{x + \mu_N}{\sigma_N} \right) - 1 \] (1.8) wobei: - \( \mu_N \): Mittelwert der ursprünglichen Normalverteilung, der eine systematische Nullpunktverschiebung kennzeichnet - \( \sigma_N \): Standardabweichung der ursprünglichen Normalverteilung - \( \Phi \): Verteilungsfunktion der standardisierten Normalverteilung ``` Image Analysis: 1. **Localization and Attribution:** - Single image on the page. 2. **Object Detection and Classification:** - The image consists primarily of text with mathematical formulas. - The text is structured with headings and subheadings to detail the context of probability distribution functions. 3. **Scene and Activity Analysis:** - The document appears to be a technical or scientific one, likely from a textbook or research paper. - The main activity involves explaining probability concepts with specific references to integral functions, transformation variables, and probability densities. 4. **Text Analysis:** - The text is predominantly in German, explaining mathematical concepts related to probability distribution functions. - Key terms include "Normalverteilung" (normal distribution), "Verteilungsfunktion" (distribution function), and "Wahrscheinlichkeitsdichte" (probability density). - Specific formulas are given: - General integral of the probability density function: \[ F_{N}(x_s) = \int_{-\infty}^{x_s} f_{N}(x)dx \] - Standard normal distribution density: \[ \varphi(u) = \frac{1}{\sqrt{2\pi}} e^{-\frac{u^2}{2}} \] - Distribution function of the standard normal distribution: \[ \Phi(u_j) = \int_{-\infty}^{u_j} \frac{1}{\sqrt{2\pi}} e^{-\frac{u^2}{2}} du \] 5. **Diagram and Chart Analysis:** - No diagrams or charts are present in the image. 6. **Product Analysis:** - Not applicable. 7. **Anomaly Detection:** - There are no noticeable anomalies in the image. 8. **Color Analysis:** - The image is monochrome, predominantly black text on a white background, which is standard for technical documents. 9. **Perspective and Composition:** - The perspective is a straightforward bird’s-eye view, typical for reading documents. - The composition follows a structured outline with headings, equations, and explanatory text. 10. **Contextual Significance:** - The contents likely form part of a larger discussion on statistical methods and probability theory, making it significant for readers needing detailed mathematical explanations. - It contributes to an in-depth understanding of probability distributions. 11. **Metadata Analysis:** - No metadata is available directly from the image. 12. **Graph and Trend Analysis:** - Not applicable. 13. **Graph Numbers:** - Not applicable. **Additional Aspects to Include:** - **Ablaufprozesse (Process Flows):** - Derivation and transformation of probability density functions. - **Prozessbeschreibungen (Process Descriptions):** - Explanation of normal distribution characteristics. - Analysis of the transformation to standard normal form. - **Typen Bezeichnung (Type Designations):** - Normalverteilung (normal distribution). - Standardnormalverteilung (standard normal distribution). - **Trend and Interpretation:** - Trends indicated pertain to the standard transformation in probability theory. - **Tables:** - No tables are included. This analysis covers the mathematical and technical details provided in the document, focusing on the explanation and formulation of normal and standard normal distributions within probability theory. #################### File: VW%2010130_DE%281%29.pdf Page: 6 Context: # Seite 6 ## VW 101 30: 2005-02 Das Bild 3 zeigt Dichtefunktionen, die sich aus der Faltung der Dichte der Normalverteilung bei verschiedenen Nullpunktverschiebungen ergeben. ![Bild 3 - Dichtefunktion der Betragverteilung 1. Art mit verschiedenen Nullpunktverschiebungen](path_to_image) ### Mittelwert und Varianz der Betragverteilung 1. Art lauten: \[ \mu = \mu_N \left( \frac{H_N}{\sigma_N} - \frac{-\mu_N}{\sigma_N} \right) + \frac{2 \cdot \sigma_N}{\sqrt{2\pi}} e^{-\frac{|\mu|}{2 \sigma^2}} \tag{1.9} \] \[ \sigma^2 = \sigma_N^2 + \mu_N^2 \tag{1.10} \] Für den Fall einer Nullpunktverschiebung \(\mu_N = 0\) ergibt sich aus (1.9) und (1.10): \[ \mu = \frac{2 \cdot \sigma_N}{\sqrt{2\pi}} \tag{1.11} \] \[ \sigma^2 = \left( \frac{1 - \frac{2}{\pi}}{2} \right) \sigma_N^2 \tag{1.12} \] Wie Bild 3 zeigt, nähert sich die Betragverteilung 1. Art mit zunehmender Nullpunktverschiebung einer Normalverteilung. Somit kann für den Fall \(\frac{\mu}{\sigma} \geq 3\) die Betragverteilung 1. Art mit guter Näherung durch eine Normalverteilung ersetzt werden. Image Analysis: ### Analysis of the Attached Visual Content #### 1. Localization and Attribution - The attached content consists of a single page. - Only one image is present on the page, which includes a diagram/graph. #### 2. Object Detection and Classification - **Image 1:** - Objects: Graph with multiple lines representing different data sets. - Key Features: The graph has labeled axes, multiple curves with different characteristics, and a legend indicating variances in data sets. #### 3. Scene and Activity Analysis - **Image 1:** - Scene: A graph illustrating different density functions. - Activities: Presentation of data showing how the folding of the density of the normal distribution results from various null point shifts. #### 4. Text Analysis - **Text in Image:** - Top of the page: "Seite 6" (Page 6), "VW 101 30: 2005-02." - Below the graph: "Das Bild 3 zeigt Dichtefunktionen, die sich aus der Faltung der Dichte der Normalverteilung bei verschiedenen Nullpunktverschiebungen ergeben." - Translation: "Figure 3 shows density functions that result from the folding of the density of the normal distribution for various null point shifts." - Graph Title: "Bild 3 - Dichtefunktion der Betragsverteilung 1. Art mit verschiedenen Nullpunktverschiebungen" - Translation: "Figure 3 - Density Function of the First Kind Distribution with Different Null Point Shifts." - Equations at the bottom with references (1.9), (1.10), etc., providing formulas for mean and variance calculations: - μ = ... (equation 1.9) - σ² = ... (equation 1.10) - Additional details are provided on calculations and implications of null point shifts. #### 5. Diagram and Chart Analysis - **Axes:** - X-axis: "Merkmalswert" (Feature Value) ranges from 0 to 6σN. - Y-axis: "Wahrscheinlichkeitdichte" (Probability Density). - **Legend and Data Visualization:** - Multiple curves indicate different μN values (μN = 0, μN = 1σN, μN = 2σN, μN = 3σN). - Each curve represents a varying null point shift, illustrating changes in the density function. - **Key Insights:** - The graph shows that as the null point shift (μN) increases, the density function changes. - The spread and peak of the curves illustrate how the distribution varies with different μN values. #### 12. Graph and Trend Analysis - **Trends:** - For μN = 0, the curve resembles a normal distribution. - As μN increases (1σN, 2σN, 3σN), the peak of the curves shifts, becoming less centralized and more spread out. - **Data Points:** - The graphs indicate a progressive shift and broadening of the distribution as μN increases. #### 13. Graph Numbers - **Data Points:** - Exact numerical values are not provided in the graph itself, but the trend illustrates a continuous and smooth transition in density functions with increasing μN. #### Process Descriptions and Contextual Significance - **Context:** - The diagram and equations provide a mathematical explanation for distribution density functions influenced by null point shifts. - **Process Descriptions:** - The text explains the derivation of mean (μ) and variance (σ²) formulas for the first kind of distribution. - It indicates that as the null point shift increases, the distribution approximates normal distribution properties, showing that for large shifts (μ/σ ≥ 3), the first kind of distribution can be effectively replaced by a normal distribution. #### Conclusion - The attached visual content gives a detailed mathematical and graphical representation of how density functions change with various null point shifts. It is clear that as shifts increase, the distributions adjust in their variance and mean, becoming comparable to regular normal distributions for large shifts. The equations and graph provide a comprehensive understanding of these changes. #################### File: VW%2010130_DE%281%29.pdf Page: 7 Context: # 3.1.3 Betragsverteilung 2. Art (Rayleigh-Verteilung) Die Betragsverteilung 2. Art ergibt sich aus den vektoriellen Beträgen der orthogonalen Komponenten \(x\) und \(y\) einer zweidimensionalen Normalverteilung, wobei für die Komponenten gleiche Standardabweichungen angenommen werden. Dieser Fall liegt bei vielen Fertigungsmerkmalen in Form radialer Abweichungen von einem betrachteten Punkt oder einer betrachteten Achse vor. Die Dichtenfunktion und die Verteilungsfunktion der Betragsverteilung 2. Art lauten allgemein: \[ f_{gZ}(r) = \frac{r}{2\pi\sigma_N^2} e^{-\frac{r^2}{2\sigma_N^2}} \quad \text{für } r \geq 0 \tag{1.14} \] \[ F_{Z}(r) = \int_{0}^{r} f_{gZ}(r) \, dr \tag{1.15} \] wobei - \(\sigma\) = Standardabweichung der orthogonalen Komponenten \(x\) und \(y\), aus denen sich die radiale Abweichung \(r\) von einem Bezugspunkt oder einer Bezugssach ergibt - \(z\) = Exzentricität: Abstand zwischen Koordinatenursprung und Häufigkeitsmittelpunkt Das Bild 4 zeigt Dichtefunktionen der Betragsverteilung 2. Art, die sich bei verschiedenen Exzentrizitäten in Einheiten von \(\sigma_N\) ergeben. ![Bild 4 - Dichtefunktionen der Betragsverteilung 2. Art mit verschiedenen Exzentrizitäten](image_link) Mittelwert und Varianz der Betragsverteilung 2. Art lauten. Image Analysis: ### Comprehensive Examination of Attached Visual Content **1. Localization and Attribution:** - **Image 1:** Positioned at the top, it contains textual descriptions of the Rayleigh distribution. - **Image 2:** Positioned at the bottom, it is a chart illustrating density functions of the Rayleigh distribution under various eccentricities. **2. Object Detection and Classification:** - **Image 1:** - Objects: Text blocks, equations - Classification: Academic text, mathematical equations - **Image 2:** - Objects: Graph, axes, legends - Classification: Statistical graph, density functions **3. Scene and Activity Analysis:** - **Image 1:** Describes the Rayleigh distribution and provides mathematical equations. The main actors are the equations and definitions of standard deviation and eccentricity. - **Image 2:** Shows a graph with multiple curves representing the density functions. The activity includes the visualization of different eccentricities. **4. Text Analysis:** - **Image 1:** Contains German text explaining the Rayleigh distribution (Betraeverteilung 2. Art), its density function, and related terms. - Key excerpts: - "Die Betragsverteilung 2. Art ergibt sich aus den vektoriellen Beträgen der orthogonalen Komponenten x und y..." - Equations (1.14) and (1.15) provide the mathematical formulations of the density function. - Definitions of "Standardabweichung" (Standard deviation) and "Exzentrizität" (Eccentricity). - **Image 2:** The text below the graph provides a description: - "Bild 4 - Dichtefunktionen der Betragsverteilung 2. Art mit verschiedenen Exzentrizitäten" translates to "Figure 4 - Density functions of the Rayleigh distribution 2nd type with different eccentricities." **5. Diagram and Chart Analysis:** - **Axes:** - Horizontal Axis (x-axis): Labeled "Merkmalswert" (Feature value) - Vertical Axis (y-axis): Labeled "Wahrscheinlichkeitsdichte" (Probability density) - **Legends:** - Different curves for z = 0, z = 1σ_N, z = 2σ_N, z = 3σ_N - **Key Insights:** - The graph shows how the probability density changes with varying eccentricity values (z). - As eccentricity increases, the peak of the density function tends to flatten and spread out more. **8. Color Analysis:** - **Dominant Colors:** Black and white (monochromatic) - Impact: A formal and academic appearance, suitable for technical and mathematical documentation. **9. Perspective and Composition:** - **Perspective:** The graph is presented in a standard view typical for academic papers. - **Composition:** Text explanations form the upper section, and the graph is centered in the lower section, allowing clear association between the explanations and the visual representation. **10. Contextual Significance:** - **Image 1:** Provides theoretical background and necessary definitions for understanding the Rayleigh distribution. - **Image 2:** Uses graphical representation to illustrate the theoretical concepts explained in the text, thus helping in visual comprehension. **12. Graph and Trend Analysis:** - **Trends:** - With increasing eccentricity (z), the density functions peak lowers and the spread increases, indicating more variability and higher spread in data points. By analyzing the density function changes with different eccentricities, one can infer the impact of such parameters on the distribution, which is crucial for applications in various fields such as signal processing and reliability engineering. #################### File: VW%2010130_DE%281%29.pdf Page: 8 Context: # Seite 8 ## VW 101 30: 2005-02 \[ \mu = \int f_{G2}(r) \cdot r \cdot dr \quad (1.16) \] \[ \sigma^2 = 2 \cdot \sigma_N^2 + z^2 - \mu^2 \quad (1.17) \] Für den Fall einer Exzentrizität \( z = 0 \) ergeben sich aus (1.14) und (1.15) Dichtefunktion und Verteilungsfunktion der Weibull-Verteilung mit dem Formparameterwert 2: \[ f_{G2}(r) = \frac{r}{\sigma_N} \cdot e^{-\left(\frac{r}{\sigma_N}\right)^2} \quad (1.18) \] \[ F_{G2}(r) = 1 - e^{-\left(\frac{r}{\sigma_N}\right)^2} \quad (1.19) \] und daraus wiederum Mittelwert und Varianz: \[ \mu = \sigma_N \cdot \sqrt{\frac{\pi}{2}} \quad (1.20) \] \[ \sigma^2 = \left(2 - \frac{\pi}{2}\right) \cdot \sigma_N^2 \quad (1.21) \] Wie Bild 4 zeigt, nähert sich die Betragsverteilung 2. Art mit zunehmender Exzentrizität einer Normalverteilung. Somit kann für den Fall \[ \frac{\mu}{\sigma} \geq 6 \quad (1.22) \] die Betragsverteilung 2. Art mit guter Näherung durch eine Normalverteilung ersetzt werden. ## 3.2 Fähigkeitensermittlung Die Fähigkeitenkennwerte \( c_n \) und \( c_{pk} \) geben an, wie gut die Fertigungsergebnisse das Toleranzintervall eines betrachteten Merkmals einhalten. Dabei wird durch den \( c_n \)-Wert nur die Fertigungsstreuung berücksichtigt. Die Fertigungslage wird durch den \( c_{pk} \)-Wert berücksichtigt. Damit lässt sich einerseits ausdrücken, welcher Wert bei einer idealen Fertigungslage möglich ist, und andererseits lässt sich durch Vergleich der beiden Werte ausdrücken, wie stark die Fertigungslage vom Sollwert abweicht. Je größer die ermittelten Fähigkeitenkennwerte sind, desto besser ist die Fertigung. Zur Ermittlung der Fähigkeitenkennwerte gibt es verschiedene Auswertemethoden, die dem jeweiligen Fall entsprechend auszuwählen sind. Da die Ermittlung der Fähigkeitenkennwerte nur aus Stichproben erfolgen kann, sind die Ergebnisse nur Schätzungen der gesuchten Werte der Grundgesamtheit und sind somit durch ein Dach-Symbol gekennzeichnet. Image Analysis: ### Image Analysis #### Localization and Attribution - **Image 1**: Located at the top of the page. Contains mathematical formulas and text. - **Image 2**: Located at the bottom portion of the page. Contains a section header and a detailed paragraph with some footnotes. #### Text Analysis - **Image 1**: - **Formulas and Equations**: - \( \mu = \int_0^r f_{32}(r) \cdot r \cdot dr \) (1.16) - \( \sigma^2 = 2r_N^2 + z^2 - \mu^2 \) (1.17) - \( f_{32}(r) = \left( \frac{r}{\sigma_N} \right) \cdot e^{-\left( \frac{r}{\sigma_N} \right)^2} \) (1.18) - \( F_{32}(r) = 1 - e^{-\left( \frac{r}{\sigma_N} \right)^2} \) (1.19) - \( \mu = \sigma_N \cdot \sqrt{\frac{\pi}{2}} \) (1.20) - \( \sigma^2 = \left( 2 - \frac{\pi}{2} \right) \cdot \sigma_N^2 \) (1.21) - \( \frac{\mu}{\sigma} \geq 6 \) (1.22) - **Description**: - The text and formulas describe the calculation of the mean (\( \mu \)) and variance (\( \sigma^2 \)) of a distribution, particularly focusing on the case with zero eccentricity. The Weibull distribution with a shape parameter of 2 is utilized, and the resulting density and distribution functions are explained and formulated. The image also notes the approximation to a normal distribution under certain conditions. - **Image 2**: - **Header**: - "3.2 Fähigkeits­ermittlung" (3.2 Capability Determination) - **Paragraph**: - Discusses the capability indices Cp and Cpk, explaining their significance in assessing the conformity of production outcomes with tolerance intervals. The text elaborates on how these indices are calculated and the information they provide about the production process and its adherence to target values. - It mentions that estimated capability indices are marked with a roof symbol and suggests this notation is for theoretical purposes and may not be necessary for practical evaluations. - **Footnotes**: - Die Kennzeichnung der geschätzten Fähigkeitskennwerte durch ein Dach-Symbol ist nur zum Verständnis der Theorie von Bedeutung, so dass bei den Auswertungen in der Praxis darauf verzichtet werden kann. (The marking of estimated capability indices with a roof symbol is only for theoretical understanding, so in practical evaluations, it can be omitted.) #### Contextual Significance - **Mathematical Context**: - The formulas and text in **Image 1** provide a detailed mathematical treatment of the calculation of statistical measures (mean and variance) in specific distribution contexts, emphasizing their approximation to well-known distributions like the normal distribution. - **Practical Context**: - **Image 2** delves into the practical aspects of quality control in manufacturing, specifically addressing how capability indices (\( C_p \), \( C_{pk} \)) are used to assess how well production processes meet specified quality targets. This section is crucial for understanding the practical application of statistical methods in quality management. ### Summary The document page integrates detailed mathematical equations and theoretical explanations of distribution functions, particularly the Weibull distribution, in its upper section. The lower section transitions to a practical discussion on the determination of capability indices, underscoring their importance in the manufacturing process and quality control. #################### File: VW%2010130_DE%281%29.pdf Page: 9 Context: # 3.2.1 Fähigkeitsermittlung bei definierten Verteilungsmodellen ## 3.2.1.1 Fähigkeitskennwerte Für ein zu untersuchendes Fertigungsmerkmal, dessen Stichprobenwerte nicht im Widerspruch mit einem theoretisch zu erwartenden Verteilungsmodell sind, werden die Fähigkeitskennwerte den jeweiligen Fall entsprechend (siehe auch Beispiele 1 und 2 in Abschnitt 5) nach folgenden Formeln geschätzt: Fähigkeitskennwerte für zweiseitig toleriertes Merkmal (nach DIN 55319, Methode M4), z.B. für Längenmaß: \[ \hat{c_m} = \frac{G_o - G_u}{x_{99.865\%} - x_{0.135\%}} \] \[ \hat{c_{mk}} = \min \left( \frac{G_o - \bar{\mu}}{x_{99.865\%} - \bar{\mu} - x_{0.135\%}} \right) \] Fähigkeitskennwerte für einseitig nach oben toleriertes Merkmal mit natürlichem unteren Grenzwert Null, z.B. für Rundlaufabweichung: \[ \hat{c_m} = \frac{G_o}{x_{99.865\%} - x_{0.135\%}} \] \[ \hat{c_{mk}} = \frac{G_o - \bar{\mu}}{x_{99.865\%} - \bar{\mu}} \] Fähigkeitskennwert für einseitig nach unten toleriertes Merkmal, z.B. für Zugfestigkeit: \[ \hat{c_{mk}} = \frac{\bar{\mu} - G_u}{\bar{\mu} - x_{0.135\%}} \] wobei \(G_o, G_u\): Höchstmaß, bzw. Mindestmaß \(\bar{\mu}\): geschätzter Mittelwert \(x_{0.135\%}, x_{99.865\%}\): Schätzwerten für Streubereichsgrenzen (Quantile, unterhalb derer der angegebene Anteil p von Messwerten liegt) Image Analysis: ### Analysis of the Provided Document Page: #### Aspect: Localization and Attribution 1. **Image Position and Numbering:** - **Image 1:** The entire document page. #### Aspect: Text Analysis 1. **Detected Text:** - The entire document contains German text with formulas and a heading. - Heading: "3.2.1 Fähigkeitsermittlung bei definierten Verteilungsmodellen" 2. **Content Analysis:** - **Heading:** - "3.2.1 Fähigkeitsermittlung bei definierten Verteilungsmodellen" translates to "Determination of Capability with Defined Distribution Models". - **Subheading:** - "3.2.1.1 Fähigkeitskennwerte" translates to "Capability Indices". - **Formulas and Descriptions:** - Several formulas calculate capability indices for various features. - The usage of parameters G_o, G_u, \(\hat{\mu}\), \(\hat{σ}_{0.135%}\), \(\hat{σ}_{99.865%}\). - Text explains the application of these formulas for bilateral tolerances, upper limit tolerances, and lower limit tolerances. - Symbols and descriptions include: - \(G_o, G_u\): High and low limits. - \(\hat{\mu}\): Estimated mean value. - \(\hat{σ}_{0.135%}, \hat{σ}_{99.865%}\): Quantile estimates for the boundaries. - **Formula Descriptions:** - Equation (2.1) and (2.2) describe a capability index formula for bilaterally tolerable characteristics. - Equations (2.3) and (2.4) show the capability index for characteristics with a natural lower limit. - Equation (2.5) deals with capability indices for characteristics with a lower limit. #### Aspect: Diagram and Chart Analysis 1. **Absent in the Document:** - No diagrams or charts are presented on the page that needs analysis. #### Aspect: Process Flows (Ablaufprozesse) 1. **Explanation of Processes:** - Step-by-step manual calculation processes for determining various capability indices are explained using mathematical formulas. #### Aspect: Perspective and Composition 1. **Perspective:** - The document is in a typical document layout view with clear sections and formulae structures. - Composition is focused on presenting information clearly with wide margins. #### Aspect: Contextual Significance 1. **The Overall Context:** - The document appears to be a technical standard or a part of a technical manual for calculating manufacturing process capabilities using statistical distribution models. - It likely targets quality assurance professionals or engineers involved in manufacturing and process design. ### Summary This document page primarily serves as a technical instruction for calculating several statistical capability indices for manufacturing processes described using clear mathematical formulas and parameters. It focuses on ensuring product quality through precise capability assessment. There are no graphs, charts, or additional images, nor are there unusual anomalies. The layout is typical of technical or standards documents, emphasizing clarity, precise formula representation, and extensive notations for contextual understanding. #################### File: VW%2010130_DE%281%29.pdf Page: 10 Context: # 3.2.1.2 Schätzung der statistischen Kenngrößen Die statistischen Kenngrößen Mittelwert \( \mu \) und Standardabweichung \( \sigma \) einer Grundgesamtheit lassen sich unabhängig vom Verteilungsmodell aus den Messwerten einer Stichprobe erwartungstreu schätzen durch \[ \hat{\mu} = \frac{1}{n_e} \sum_{i=1}^{n_e} x_i \tag{2.6} \] \[ \hat{\sigma}^2 = s^2 = \frac{1}{n_e - 1} \sum_{i=1}^{n_e} (x_i - \bar{x})^2 \tag{2.7} \] wobei \[ n_e = n - n_a : \text{effektiver Stichprobenumfang} \tag{2.8} \] \[ n : \text{gewählter Stichprobenumfang} \] \[ n_a : \text{Anzahl der Ausreißer} \] \[ x_i : \text{i-ter Merkmalwert} \] Im Fall auswertender Daten in Form einer Häufigkeitsverteilung klassierter Messwerte, z.B. aus manuellen Aufzeichnungen in Form von Strichen in einer Klasseneinteilung des Werbebereichs (Strichliste), lassen sich die Kenngrößen \( \mu \) und \( \sigma \) schätzen durch \[ \hat{\mu} = \frac{1}{n_e} \sum_{k=1}^{K} a_k \cdot x_k \tag{2.9} \] \[ \hat{\sigma} = \frac{1}{\sqrt{n_e - 1}} \sqrt{\sum_{k=1}^{K} a_k \cdot (x_k - \bar{x})^2} \tag{2.10} \] wobei \[ \bar{x} : \text{Mittelwert der k-ten Klasse} \] \[ a_k : \text{absolute Häufigkeit der Messwerte in der k-ten Klasse (ohne Ausreißer)} \] \[ K : \text{maximale Anzahl der Messwertklassen} \] # 3.2.1.3 Schätzung der Streubereichsgrenzen Die Streubereichsgrenzen hängen vom Verteilungsmodell ab und werden wie folgt geschätzt: **Streubereichsgrenzen der Normalverteilung:** Im Fall einer Normalverteilung als passendes Verteilungsmodell ergeben sich aus den nach (2.6) und (2.7) bzw. (2.9) und (2.10) ermittelten Werten \( \mu \) und \( \sigma \) Schätzwerte für die Streubereichsgrenzen \[ x_{0.9965} \leq \mu \pm 3 \hat{\sigma} \tag{2.11} \] die wiederum in Formel (2.1) und (2.2) eingesetzt die klassischen Formeln zur Berechnung der Fähigkeitskennwerte ergeben (siehe auch Beispiel 1 im Abschnitt 5). Image Analysis: ### Image Analysis #### Localization and Attribution - **Image 1** is located on a single-page document that is indexed as "Seite 10" in the upper-left corner, indicating it is page 10. #### Text Analysis - The document is predominantly composed of text written in German, with sections, equations, and formulae relating to statistical concepts. - Key headings and text: - **Main Section: "3.2.1.2 Schätzung der statistischen Kenngrößen"** - Translation: "Estimation of statistical parameters" - **Sub Section: "Schätzung der Mittelwert und Standardabweichung"** - Translation: "Estimation of mean value and standard deviation" - Various formulae and their explanations are presented. - **Equations:** - (2.6): \(\hat{\mu} = \frac{1}{n_e} \sum_{i=1}^n X_i\) - Describes the estimation of the mean. - (2.7): \(\hat{\sigma}^2 = \frac{1}{n_e - 1} \sum_{i=1}^n (X_i - \bar{X})^2\) - Describes the estimation of variance. - (2.9) and (2.10): Additional formulae extending for grouped data. - Down to: \(\hat{\sigma_{99,865}} = \hat{\mu} \pm 3\sigma\) - Indicates calculation incorporating deviation. #### Diagram and Chart Analysis - No diagrams or charts are present in this image. #### Process Descriptions (Prozessbeschreibungen) - **Process Flows:** - The text develops the formula for the estimation of statistical parameters step by step. - The process involves identifying the sample size, calculating mean, variance, and then adjusting these calculations according to the nature of the data (e.g., in the case of grouped data). #### Typen Bezeichnung (Type Designations) - **Statistical Terms:** - \(\hat{\mu}\): Estimation of mean (Mittelwert) - \(\hat{\sigma}^2\): Estimation of variance (Standardabweichung) - \(n\): Size of sample (Stichprobenumfang) - Various variables for data points and frequencies are used in the given formulae. #### Perspective and Composition - The perspective is directly front-facing, typical of a scanned document or a digitally created page. - The composition is set in a structured layout geared towards readability, especially for mathematical and technical documentation. ### Contextual Significance - **Overall context**: This document appears to be a technical guide or academic text on statistical methods, particularly focusing on estimation techniques for statistical parameters. - **Contribution to the overall message**: The image supplies detailed processes and formula derivations essential to statistically analyzing data, a crucial part of research methodologies where accuracy and precision in calculations are emphasized. ### Metadata Analysis - No metadata is available directly from the image content. Overall, the primary function of this document image is educational and technical, providing in-depth statistical formulas and their derivations essential for understanding statistical estimation processes. The text is highly structured, focusing clearly on the explanation of mean and variance estimations within statistics. #################### File: VW%2010130_DE%281%29.pdf Page: 11 Context: # Streubereichsgrenzen der Betragsverteilung 1. Art Zur Ermittlung der Streubereichsgrenzen für eine Betragsverteilung 1. Art werden zunächst nach Formel (2.6) und (2.7) bzw. (2.9) und (2.10) die Kenngrößen μ und σ geschätzt. Für den Fall μ/σ < 3 werden dann aus den geschätzten Kenngrößen μ und σ die gesuchten Parameterwerte μₑ und σₑ der anzupassenden Betragsverteilung 1. Art in der folgenden Weise geschätzt: Aus Gleichung (1.9) erhält man die Funktion \[ \frac{\mu}{\sigma} = v \cdot \sqrt{\left(\frac{N}{n}\right) \cdot \left(\frac{\partial \mu}{\partial N}\right) - \left(\frac{N - n}{N}\right) \cdot \left(\frac{\partial \mu}{\partial N}\right) + \frac{2}{\sqrt{2\pi}} \cdot \frac{f(a)}{f(b)}} \] Mit Gleichung (1.10) ergibt sich daraus die Funktion \[ \frac{\sigma}{\bar{g}} = \frac{\beta\mu}{\sigma} \cdot \sqrt{\left(\frac{\partial \mu}{\partial N}\right) + \left(\sqrt{\frac{N}{n}}\right) - \left(\frac{N - n}{N}\right) \cdot \left(\frac{\partial \mu}{\partial N}\right)}^2 \] Aus den Gleichungen (1.11) und (1.12) ergibt sich die Bedingung \[ \frac{\mu}{\sigma} = \frac{\sqrt{2}}{\sqrt{n}} = 1,3236 \] Die gesuchten Parameterwerte der Betragsverteilung 1. Art lassen sich somit unter der Bedingung (2.14) durch \[ \sigma_N = \sigma \cdot \frac{1 + \left(\frac{\mu}{\sigma}\right)^2}{1 + \left(\frac{\sigma}{\sigma}\right)^2} \] \[ \mu_N = \xi_{B} \left(\frac{\mu}{\sigma}\right) \cdot \sigma_N \] schätzen, wobei \[ \xi_{B} \left(\frac{\mu}{\sigma}\right) = \text{inverse Funktion von (2.13)} \] Für den Fall, dass das Verhältnis μ/σ aufgrund von Zufallsabweichungen der Stichprobenkenntnissen kleiner ist als der Grenzwert 1,3236 aus der Bedingung (2.14), wird das Verhältnis μ/σ auf diesen Grenzwert gesetzt, bei dem sich die folgenden Parameterwerte ergeben: \[ \mu_N = 0 \quad \text{und nach Formel (1.12)} \] \[ \sigma_N = \frac{\pi}{\sqrt{2}} \cdot 1,659 \] Image Analysis: **Text Analysis:** 1. **Localization and Attribution:** - The content is a single page, labeled "Seite 11," which translates to "Page 11" in English. - The document is identified with "VW 101 30: 2005-02," likely indicating a standard or technical document from February 2005. 2. **Text Analysis:** - The primary heading states: "Streubereichsgrenzen der Betragsverteilung 1. Art," which translates to "Scatter range limits of the absolute distribution of the 1st kind." - The page describes the process of determining the scatter range limits for an absolute distribution of the first kind, using various equations and conditions. 3. **Equations and Mathematical Content:** - Equations labeled (2.12), (2.13), (2.14), (2.15), (2.16), and (2.17) are provided throughout the text, specifying various functions and conditions related to statistical parameters like mean (μ) and standard deviation (σ). 4. **Key Mathematical Concepts:** - The document discusses assessing statistical properties using formulas such as: - \(\frac{\mu}{\sigma} = \sqrt{\frac{2}{\pi}} \cdot \frac{1}{1,3236} \) - \(\sigma_N = \sigma \cdot \sqrt{ \frac{ 1 + \left(\frac{\mu}{\sigma}\right)^2}{ 1 + \xi_{gr} \left(\frac{\mu}{\sigma}\right)^2} } \) - \(\mu_N = \xi_{gr} \left(\frac{\mu}{\sigma}\right) \cdot \sigma_N\) - \(\frac{\mu}{\sigma} = \frac{\pi}{\sqrt{\pi - 2}} \) for a specific condition \(\frac{\mu}{ \sigma} < 1.659 \) **Conclusion:** This single-page excerpt appears to be from a technical document detailing the parameters and mathematical methods for analyzing statistical distributions, specifically focusing on the first kind of absolute distribution. The provided equations assist in estimating parameters like mean and standard deviation for various conditions. #################### File: VW%2010130_DE%281%29.pdf Page: 12 Context: # Seite 12 VW 101 30: 2005-02 Der Zusammenhang zwischen den Parameterwerten \(\mu_N\) und \(\alpha_N\) der Betragsverteilung 1. Art und den statistischen Kennwerten \(\mu\) und \(\sigma\) ist in Bild 5 auf \(\sigma\) bezogen grafisch dargestellt. ## Bild 5 - Relative Parameterwerte der Betragsverteilung 1. Art in Abhängigkeit von der relativen Lage ![Relative Parameterwerte](path/to/image5.png) Für die angepasste Betragsverteilung 1. Art lassen sich dann die Streubreichsgrenzen numerisch ermitteln, deren Abhängigkeiten von der relativen Lage in Bild 6 dargestellt sind. ## Bild 6 - Relative Streubreichsgrenzen der Betragsverteilung 1. Art in Abhängigkeit von der relativen Lage ![Relative Streubreichsgrenzen](path/to/image6.png) Image Analysis: ### Localization and Attribution: 1. **Image 1**: Located at the top half of the page. 2. **Image 2**: Located at the bottom half of the page. ### Object Detection and Classification: #### Image 1: - **Objects**: Graph - **Categories**: - x-axis labeled "relative Lage μ / σ" - y-axis labeled "relativer Verteilungsparameter" - Two plotted lines labeled as \(\mu_{N1}\ / \sigma\) and \(\sigma_{N1} / \sigma\) #### Image 2: - **Objects**: Graph - **Categories**: - x-axis labeled "relative Lage μ / σ" - y-axis labeled "relative Streubereichsgrenze" - Two plotted lines labeled as \(X_{0,8685}σ / σ\) and \(X_{0,1315}σ / σ\) ### Scene and Activity Analysis: #### Image 1: - **Scene**: A graphical representation depicting relative parameter values for the 1st type of value distribution as a function of relative position. - **Activity**: The plotting of two distinct curves on a graph. #### Image 2: - **Scene**: A graphical representation showing relative scatter range limits for the 1st type of value distribution in relation to relative position. - **Activity**: The plotting of two distinct lines on a graph to indicate scatter range boundaries. ### Text Analysis: #### Image 1: - **Detected Text**: - Title: "Bild 5 - Relative Parameterwerte der Betragsverteilung 1. Art in Abhängigkeit von der relativen Lage" - Graph Labels: \(\mu_{N1} / σ\) and \(\sigma_{N1} / σ\) #### Image 2: - **Detected Text**: - Title: "Bild 6 - Relative Streubereichsgrenzen der Betragsverteilung 1. Art in Abhängigkeit von der relativen Lage" - Graph Labels: \(X_{0,8685}σ / σ\) and \(X_{0,1315}σ / σ\) ### Diagram and Chart Analysis: #### Image 1: - **Axes**: - x-axis: "relative Lage μ / σ" - y-axis: "relativer Verteilungsparameter" - **Scales**: - x-axis ranges from 1.2 to 3.0 in consistent increments. - y-axis ranges from 0.0 to 3.5. - **Legends**: - \(\mu_{N1} / σ\): Indicates the relative position parameter. - \(\sigma_{N1} / σ\): Represents the relative spread parameter. - **Key Insights**: - Identify the relationship between the distribution parameters as the relative position varies. #### Image 2: - **Axes**: - x-axis: "relative Lage μ / σ" - y-axis: "relative Streubereichsgrenze" - **Scales**: - x-axis ranges from 1.2 to 3.0 in consistent increments. - y-axis ranges from 0 to 7. - **Legends**: - \(X_{0,8685}σ / σ\): Upper scatter boundary. - \(X_{0,1315}σ / σ\): Lower scatter boundary. - **Key Insights**: - Illustrate how the scatter boundaries change with respect to the relative position. ### Graph and Trend Analysis: #### Image 1: - **Analysis**: - The graph shows two lines, with one (\(\mu_{N1} / σ\)) increasing steadily while the other (\(\sigma_{N1} / σ\)) shows a non-linear decrease before stabilizing. - **Trends**: - \(\mu_{N1} / σ\) trend is upward indicating an increase in the parameter with relative position. - \(\sigma_{N1} / σ\) decreases initially and then stabilizes suggesting a complex initial relationship before stabilization. #### Image 2: - **Analysis**: - The graph shows two nearly parallel lines with slight positive trends, indicating upper and lower scatter boundaries. - **Trends**: - Both lines maintain a nearly constant distance apart, suggesting upper and lower bounds that are relatively stable. ### Graph Numbers: #### Image 1: 1. **\(\mu_{N1} / σ\) Data Points**: - (1.2, range from 0 to 3.5) 2. **\(\sigma_{N1} / σ\) Data Points**: - (1.4, range from 0 to 1.5) #### Image 2: 1. **\(X_{0,8685}σ / σ\) Data Points**: - (1.4, range from 0 to 7) 2. **\(X_{0,1315}σ / σ\) Data Points**: - (1.2, range from 0 to 4) ### Typen Bezeichnung (Type Designations): #### Image 1 and Image 2: - The types or categories specified are: - 1st type of value distribution. ### Trend and Interpretation: #### Image 1: - **Trend**: Increases for \(\mu_{N1} / σ\) with stabilization for \(\sigma_{N1} / σ\). - **Interpretation**: Indicates how distribution parameters behave proportionally to relative position. #### Image 2: - **Trend**: Stable upper and lower scatter boundaries. - **Interpretation**: Reflects consistent scatter range bound stability over the varied relative position. By covering the mentioned aspects, the above examination gives a comprehensive view of the visual content provided. #################### File: VW%2010130_DE%281%29.pdf Page: 13 Context: ``` Zur direkten Ermittlung der Kenngrößen \(\mu\) und \(\sigma\) aus den Kenngrößen \(j\) und \(k\) kann für \(1,3236 < \frac{\sigma}{\hat{j}} < 3\) auch die folgende Näherung als inverse Funktion von (2.13) mit ausreichender Genauigkeit (auf \( \bezüglich \) Fehler kleiner als 0,01) verwendet werden: \[ \hat{\epsilon} = 1,64 \cdot \left(\frac{\hat{j}}{\sigma}\right)^{0.296} + 0,634 \cdot \left(\frac{\hat{j}}{\sigma}\right)^{0.196} \] \[ (2.18) \] Zudem kann die Ermittlung der Streubreitengrenzen für \(1,3236 < \frac{\sigma}{\hat{j}} < 3\) direkt mit Hilfe der folgenden Näherung (auf \( \bezüglich \) Fehler kleiner als 0,02) erfolgen: \[ \hat{\xi}_{0.969} = \widehat{\epsilon} \, \cdot \, \left(\frac{\sigma}{\hat{j}}\right)^{-2.47} \cdot \left( \frac{\hat{j}}{\sigma}\right)^{0.67} + 2.505 \cdot \left( \frac{\hat{j}}{\sigma}\right)^{0.332} + 3,5711 \] \[ (2.19) \] \[ \hat{\xi}_{0.031} = 0.018 \cdot \left(\frac{\hat{j}}{\sigma}\right)^{1.236} + 0.0028 \] Für \(| \frac{j}{\sigma} | \ge 3\) erfolgt die Berechnung der Streubreitengrenzen nach Formel (2.11). ### Streubreitengrenzen der Betragsverteilung 2. Art: Zur Ermittlung der Streubreitengrenzen für eine Betragsverteilung 2. Art (siehe auch Beispiel 2 im Abschnitt 5) werden zunächst nach Formel (2.6) und (2.7) bzw. (2.9) und (2.10) die Kenngrößen \(j\) und \(k\) geschätzt. Für den Fall \(| \frac{j}{\sigma} | < 6\) werden dann aus den geschätzten Kenngrößen \(j\) und \(k\) die gesuchten Parameterwerte \(z\) und \( \alpha \) der anzupassenden Betragsverteilung 2. Art in der folgenden Weise ermittelt: Aus den Gleichungen (1.14) und (1.16) erhält man die Funktion \[ \frac{\hat{\mu}}{\hat{\sigma}} = \frac{z}{\sqrt{2\pi}} \cdot \int_{0}^{\theta} \left(\frac{z}{\sigma}\right) \cdot \left( \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} z^2} \right) d\alpha \, dv \] \[ (2.20) \] wobei \[ v = \frac{r}{\sigma} \] \[ (2.21) \] Mit Gleichung (1.17) ergibt sich daraus die Funktion \[ \frac{\hat{\mu}}{\hat{\sigma}} = \sqrt{\frac{z \cdot \hat{j}}{\hat{\sigma}}} \cdot \left( \sqrt{z} - \left(\frac{z}{\hat{\sigma}}\right) \right) \] \[ (2.22) \] Aus den Gleichungen (1.20) und (1.21) ergibt sich die Bedingung \[ \frac{z}{\sigma} = \frac{z}{4 \cdot \pi} = 1,9131 \] \[ (2.23) \] ``` Image Analysis: ### Image Analysis #### 1. Localization and Attribution: - **Single image**: The page contains one full-page image. - **Image Number**: Image 1. #### 2. Object Detection and Classification: - **Objects Identified**: - Blocks of text - Formulas and mathematical equations - **Classification**: - Category: Text and Mathematical expressions - **Key Features**: - The page predominantly features German text and complex mathematical formulas. #### 4. Text Analysis: - **Text Detection and Extraction**: - The image contains extensive text written in German. - Example text: - "Zur direkten Ermittlung der Kennwerte..." - "Streebreichsgrenzen der Beitragsverteilung 2. Art:" - **Content Analysis**: - The page appears to be a technical document or manual, possibly related to statistical analysis or engineering. - The text discusses methods to determine certain coefficients and parameters, likely in a scientific or engineering context. - Significant use of mathematical formulas indicates detailed procedural or methodological instructions. #### 5. Diagram and Chart Analysis: - **Mathematical Equations**: - Multiple mathematical equations are used throughout. - Examples include integrals and equations involving standard deviations and parameters (e.g., \(\hat{\xi}\), \(\overbar{\sigma}\)). #### 10. Contextual Significance: - **Contribution to Overall Message**: - The image seems to be an excerpt from a technical manual or report. - The detailed formulas suggest it is providing a method for precise calculation or statistical evaluations, potentially for quality control or distribution analysis. #### 12. Graph and Trend Analysis: - **Analysis of Formulas and Calculations**: - The formulas indicate calculations are precise, aiming for determined accuracy (\( \epsilon \)). - The formulas include complex integrals and mathematical symbols, indicating advanced statistical methods. ### Additional Insights: #### Ablaufprozesse (Process Flows): - The document outlines specific procedural steps for mathematical determination, suggesting a standardized method for engineers or scientists to follow. #### Prozessbeschreibungen (Process Descriptions): - Detailed descriptions of the mathematical formulas and their appropriate applications are provided, aiming to foster precision in statistical or engineering calculations. #### Typen Bezeichnung (Type Designations): - Different types of error terms and statistical boundaries (e.g., relative errors, distribution boundaries) are specified and described. ### Summary: - The page analyzed (Image 1) is part of a technical manual likely focused on statistical methods or engineering principles. It contains detailed German text discussing precise mathematical procedures and methodologies for accurately determining statistical parameters and coefficients. The content is dense with mathematical equations and integrals, indicating it is designed for an audience well-versed in advanced mathematics and related applications. #################### File: VW%2010130_DE%281%29.pdf Page: 14 Context: # Seite 14 VW 101 30: 2005-02 Die gesuchten Parameterwerte der Betragsverteilung 2. Art lassen sich somit unter der Bedingung (2.23) durch \[ \hat{d}_{N} = \hat{d} \cdot \frac{1 + \left( \frac{\hat{\beta}}{\hat{d}} \right)^{2}}{2 + \left( \frac{\hat{\epsilon}}{\hat{d}} \right)^{2}} \quad (2.24) \] \[ \hat{z} = \hat{z}_{2} \cdot \hat{d}_{N} \quad (2.25) \] schätzen, wobei \[ \hat{z}_{2} = \frac{\hat{\beta}}{\hat{d}} : \text{inverse Funktion von (2.22)} \] Für den Fall, dass das Verhältnis \(\hat{\beta} / \hat{d}\) aufgrund von Zufallsabweichungen der Stichprobenkenngrößen kleiner ist als der Grenzwert 1,9131 aus der Bedingung (2.23), wird das Verhältnis \(\hat{\beta} / \hat{d}\) auf diesen Grenzwert gesetzt, bei dem sich die folgenden Parameterwerte ergeben: \[ \hat{z} = 0 \quad \text{und nach Formel (1.21)} \] \[ \hat{d}_{N} = \sqrt{\frac{2}{4 - \pi}} \cdot \hat{d} = 1,526 \cdot \hat{d} \quad (2.26) \] Der Zusammenhang zwischen den Parameterwerten \(z\) und \(\hat{d}\) der Betragsverteilung 2. Art und den statistischen Kennwerten \(\mu\) und \(\sigma\) ist in Bild 7 auf der nächsten Seite grafisch dargestellt. ![Bild 7 - Relative Parameterwerte der Betragsverteilung 2. Art in Abhängigkeit von der relativen Lage](path/to/image) **Bild 7 - Relative Parameterwerte der Betragsverteilung 2. Art in Abhängigkeit von der relativen Lage** relative Lage \( \mu / \sigma \) Image Analysis: **Analysis of the Visual Content** **Image Localization and Attribution:** - There is one image on the page, referred to as Image 1. **Object Detection and Classification:** - Image 1 contains a graph, mathematical equations, and a text explaining the equations and the graph. **Text Analysis:** - **Top of the Page:** - Subtitle: "Seite 14" (Page 14) - Document identifier: "VW 101 30: 2005-02" - **Mathematical Equations:** - The mathematical text appears to be explaining parameter values of a certain distribution. Equations (2.24), (2.25), and (2.26) are referenced. - Supporting text mentions conditions and critical values for parameters µ (mean), σ (standard deviation), and related parameters. - **Graph Caption:** - "Bild 7 - Relative Parameterwerte der Betragsverteilung 2. Art in Abhängigkeit von der relativen Lage" - Translation: "Figure 7 - Relative parameter values of the magnitude distribution of the 2nd kind depending on the relative position." **Diagram and Chart Analysis:** - **Type:** Line graph. - **Axes:** - X-axis labeled "relative Lage µ / σ" (relative position µ / σ), ranges from 1.5 to 6.0. - Y-axis labeled "relativer Verteilungsparameter" (relative distribution parameter), ranges from 0 to 7. - **Data and Trends:** - The graph has two curves representing \( \frac{Z}{\sigma} \) and \( \frac{\sigma_N}{\sigma} \). - \( \frac{Z}{\sigma} \) increases monotonically. - \( \frac{\sigma_N}{\sigma} \) displays a trend starting low and increasing before plateauing at higher values. **Perspective and Composition:** - **Perspective:** - The image is a frontal view of a page, ensuring ease of reading and analysis. - **Composition:** - The text explains the context and equations are placed above the graph. - The graph stands alone at the bottom, clear and uncluttered, making it easy to interpret. **Contextual Significance:** - **In the Document:** - This page, labeled "Seite 14," is part of a larger document, suggesting it is in the middle of a section discussing statistical distribution parameters. - The graph (Figure 7) visually represents the relationship between relative positions and distribution parameters, reinforcing the equations and textual explanations provided above it. **Metadata Analysis:** - No metadata such as capture date or camera settings are available from the image. The content likely originates from a scanned or digital academic or technical document. **Graph Numbers:** - The precise data points on the curves are not explicitly given in the graph but are typically interpolated within the drawn curves. --- This detailed examination should help in understanding the context and significance of the provided page, with a focus on statistical distribution analysis. If there's any more specific aspect or deeper analysis desired, feel free to ask! #################### File: VW%2010130_DE%281%29.pdf Page: 15 Context: ```markdown Für die angepasste Betragverteilung 2. Art lassen sich dann die Streubereichsgrenzen numerisch ermitteln, deren Abhängigkeiten von der relativen Lage in Bild 8 dargestellt sind. ### Bild 8 - Relative Streubereichsgrenzen der Betragverteilung 2. Art in Abhängigkeit von der relativen Lage | relative Lage \( \mu / \sigma \) | relative Streubereichsgrenze | |-----------------------------------|-------------------------------| | 1.5 | 0.8 | | 2.0 | 2.1 | | 2.5 | 4.0 | | 3.0 | 5.5 | | 3.5 | 7.0 | | 4.0 | 7.5 | | 4.5 | 8.0 | | 5.0 | 9.0 | | 5.5 | 8.0 | | 6.0 | 7.0 | Zur direkten Ermittlung der Kennwerte \( z \) und \( \sigma_N \) aus den Kennwerten \( \mu \) und \( \sigma \) kann für \( 1.9131 \leq \mu / \sigma < 6 \) auch die folgende Näherung als inverse Funktion von (2.22) mit ausreichender Genauigkeit (auf bezogenen Fehler kleiner als 0.02) verwendet werden: \[ \hat{z}_{2,2} \left( \frac{\mu}{\sigma} \right) = 2.1 \left( \frac{\mu}{\sigma} - 1.9131 \right)^{0.343} + 0.466 \left( \frac{\mu}{\sigma} - 1.9131 \right)^{1.22} \tag{2.27} \] Zudem kann die Ermittlung der Streubereichsgrenzen für \( 1.9131 \leq \mu / \sigma < 6 \) direkt mit Hilfe der folgenden Näherung (auf bezogenen Fehler kleiner als 0.03) erfolgen: \[ \hat{x}_{90.865} = 2.6 \exp \left( -\left( \frac{\mu}{\sigma} - 1.7031 \right) \cdot 0.8 \right) + 1.425 \left( \frac{\mu}{\sigma} - 1.9131 \right)^{0.9} - 2.1206 \tag{2.28} \] Für \( \mu / \sigma \geq 6 \) erfolgt die Berechnung der Streubereichsgrenzen nach Formel (2.11). ``` Image Analysis: ### Analysis of Attached Visual Content #### 1. **Localization and Attribution:** - **Image Position:** There is a single image located at the top of the page, just beneath the text. This image will be referred to as **Image 1** for the purpose of this analysis. #### 4. **Text Analysis:** - **Detected Text:** - **ToprightText:** - "Seite 15" - "VW 101 30: 2005-02" - **Caption Below the Graph:** - "Bild 8 - Relative Streubereichsgrenzen der Betragsverteilung 2. Art in Abhängigkeit von der relativen Lage" - **Main Body Text:** - "Für die angepasste..." - "Zur direkten Ermittlung..." - ... - **Text Significance:** - The text in the image explains the methodology and findings related to the relative scatter band limits for a certain type of distribution, dependent on relative location (\(\mu/\sigma\)). - Mathematical formulas and conditions are provided to calculate the scatter band limits (\(\epsilon\)). #### 5. **Diagram and Chart Analysis:** - **Graph Analysis:** - **Axes:** - **X-Axis:** Relative Lage \( \mu / \sigma \) (Relative Location). - **Y-Axis:** Relative Streubereichsgrenze (Relative Scatter Band Limit). - **Scales:** - **X-Axis:** Range from 1.5 to 6.0 in increments of 0.5. - **Y-Axis:** Range from 0 to 9 in increments of 1. - **Legends and Data Points:** - **\( X_{0.8655}/c \):** Represents one set of data points; generally increasing trend. - **\( X_{0.135}/c \):** Represents another set of data points; also generally increasing but slower. - **Key Insights:** - The graph shows how the relative scatter band limits change with the relative location. - Both data sets (\( X_{0.8655}/c \) and \( X_{0.135}/c \)) increase with increasing \( \mu / \sigma \), indicating a positive relationship between these variables. #### 13. **Graph Numbers:** - **Data Points from Graph:** - **\( X_{0.8655}/c \):** - At \( \mu / \sigma = 2.0 \): Approx. 4 - At \( \mu / \sigma = 3.0 \): Approx. 6 - At \( \mu / \sigma = 4.0 \): Approx. 6.5 - At \( \mu / \sigma = 5.0 \): Approx. 7.5 - At \( \mu / \sigma = 6.0 \): Approx. 8 - **\( X_{0.135}/c \):** - At \( \mu / \sigma = 2.0 \): Approx. 1 - At \( \mu / \sigma = 3.0 \): Approx. 2 - At \( \mu / \sigma = 4.0 \): Approx. 2.5 - At \( \mu / \sigma = 5.0 \): Approx. 3 - At \( \mu / \sigma = 6.0 \): Approx. 4 #### **Additional Aspects to Include:** - **Ablaufprozesse (Process Flows):** - The flow from calculating scatter band limits using direct measurements and approximations is depicted with conditions and formulas, showing a methodological approach to derivations. - **Prozessbeschreibungen (Process Descriptions):** - Detailed process descriptions are provided for calculating the scatter band limits, emphasizing on different conditions and respective formulas to use. - **Typen Bezeichnung (Type Designations):** - Types or categories described in the formulas, such as \(\epsilon_{BZ}\) and data points like \( X_{0.8655}/c \) and \( X_{0.135}/c \). - **Trend and Interpretation:** - The trend shows increasing scatter band limits with increasing relative location, suggesting variability depends significantly on the location within the distribution. ### Conclusion: The visual content primarily revolves around the analysis of relative scatter band limits against the relative location for a type of distribution. The graph displays a clear positive relationship between these two variables, supported by detailed formulas and procedural descriptions in the text to compute these limits. #################### File: VW%2010130_DE%281%29.pdf Page: 16 Context: # 3.2.2 Fähigkeitsermittlung bei nicht definierten Verteilungsmodellen Lässt sich einem Fertigungsmerkmal kein passendes Verteilungsmodell zuordnen, oder widersprechen die Messwerte der entnommenen Stichprobe dem angenommenen Verteilungsmodell, so erfolgt eine verteilungsfreie Schätzung der Fähigkeitskennwerte nach der Spannweitenmethode in der folgenden modifizierten Form unter Berücksichtigung des Stichprobenumfangs (siehe auch Beispiel 1 in Abschnitt 5): ## Fähigkeitskennwerte für zweisided toleriertes Merkmal: \[ \hat{c}_{m} = \frac{G_{o} - G_{u}}{\bar{x}_{o} - \bar{x}_{u}} \tag{2.29} \] \[ \hat{c}_{mk} = \min \left( \frac{G_{o} - \bar{x}_{o}}{G_{u} - G_{l}}, \frac{\bar{x}_{o} - \bar{x}_{s}}{x_{90s} - G_{l}} \right) \tag{2.30} \] ## Fähigkeitskennwerte für einseitig nach oben toleriertes Merkmal mit natürlichem unteren Grenzwert Null: \[ \hat{c}_{m} = \frac{G_{o}}{\bar{x}_{o} - \bar{x}_{u}} \tag{2.31} \] \[ \hat{c}_{mk} = \frac{G_{o} - \hat{x}_{mk}}{\bar{x}_{o} - x_{90s}} \tag{2.32} \] ## Fähigkeitskennwerte für einseitig nach unten toleriertes Merkmal: \[ \hat{c}_{mk} = \frac{x_{90s} - G_{u}}{x_{90s} - \bar{x}_{u}} \tag{2.33} \] wobei: - \(\bar{x}_{o}, \bar{x}_{u} :\) Schätzerwerte der oberen und unteren Streubereichsgrenze - \(\hat{x}_{90s} :\) Schätzwert des 50%-Quantils Im Fall von Einzelwerten ist: \[ \hat{x}_{90s} = \bar{x} \tag{2.34} \] wobei \(\bar{x} :\) Medianwert, der Wert, der in der Mitte einer geordneten Folge von Messwerten liegt. Die Schätzung der Streubereichsgrenzen erfolgt durch: \[ \bar{x}_{o} \ \bar{x}_{u} = x_{c} \pm k \cdot \frac{R}{2} \tag{2.35} \] wobei 5) Es handelt sich hierbei nur in etwas anderer Darstellung um die gleiche Berechnungsmethode wie in der bisherigen VW-Betriebsmitteilungsvorschrift BV 1.40 für nicht normalverteilte Merkmale. Image Analysis: ### Analysis of the Attached Visual Content 1. **Localization and Attribution:** - **Image Position:** The visual content is a single page, so it is designated as **Image 1**. 2. **Text Analysis:** - **Text Content Overview:** - **Title:** "Fähigkeitsermittlung bei nicht definierten Verteilungsmodellen" - **Sections/Headings:** - "Seite 16" (indicates page number 16) - "VW 101 30: 2005-02" (likely a document identifier or version) - "3.2.2 Fähigkeitsermittlung bei nicht definierten Verteilungsmodellen" - **Formulas and Equations:** The document includes several mathematical formulas labeled with equations numbers (e.g., (2.29), (2.30), etc.). - **Detailed Content:** The content explains different statistical parameters, estimation methods, and tolerance limits for capability determination with undetermined distribution models. 3. **Diagram and Chart Analysis:** - **Formulas and Equations:** - Several equations describe the determination and estimation of capability indices for different scenarios (e.g., two-sided tolerance, one-sided tolerance with natural lower boundary at zero). - **Equations Overview:** - Equation (2.29) for two-sided tolerance: \[ \hat{c}_m = \frac{G_o - G_u}{\bar{x}_o - \bar{x}_u} \] - Equation (2.30) for a minimized capability index: \[ \hat{c}_{mk} = \min \left( \frac{G_o - \bar{x}_{50\%}, \bar{x}_{95\%} - G_u}{\bar{x}_o - \bar{x}_u} \right) \] - Equations (2.31) to (2.35) for other parameter estimations. 4. **Prozessbeschreibungen (Process Descriptions):** - The text describes statistical process estimations and calculations for capability determination when specific distribution models are undefined. It includes methods to estimate upper and lower scattering boundaries and outlines processes for individual value estimation. 5. **Typen Bezeichnung (Type Designations):** - The document categorizes different types of estimations: - For two-sided tolerance limits. - For one-sided tolerance limits with a natural boundary. - For one-sided tolerance limits without a natural boundary. 6. **Text Analysis:** - **Significance:** The text is a technical description intended for a specialized audience, likely quality engineers or statisticians working within manufacturing or production environments, dealing with capability analysis and quality control. 7. **Contextual Significance:** - **Document Context:** The page appears to be part of a larger technical document or manual related to quality management processes within Volkswagen (indicated by "VW"). - **Contribution:** This section of the document explains statistical methods for quality control, which are crucial for maintaining product standards and conforming to production requirements. Given the technical nature and the presence of mathematical formulas and specialized vocabulary, the content is primarily valuable for professionals in the quality control and assurance domain, providing detailed methodologies for capability assessment without predefined models. #################### File: VW%2010130_DE%281%29.pdf Page: 17 Context: ``` x_c = \frac{x_{max} + x_{min}}{2} \tag{2.36} R = x_{max} - x_{min} \quad \text{Spannweite} \tag{2.37} x_{max}, x_{min} : \text{maximaler bzw. minimaler Messwert der effektiven Gesamtstichprobe} Durch den Korrekturfaktor k = \frac{6}{d_n} \tag{2.38} wird dabei der effektive Stichprobenumfang n_e berücksichtigt, wobei d_n : \text{Erwartungswert der w-Verteilung}^6 Für einige Stichprobenumfänge n_e ist der Wert d_n in Tabelle 1 angegeben. # Tabelle 1 - Erwartungswert der w-Verteilung in Abhängigkeit von n_e | n_e | d_n | |-----|------| | 20 | 3,74 | | 25 | 3,93 | | 30 | 4,09 | | 35 | 4,21 | | 40 | 4,32 | | 45 | 4,42 | | 50 | 4,50 | Für Stichprobenumfänge, die größer als 20 sind, können die Erwartungswerte der w-Verteilung nach der folgenden Näherungsformel ermittelt werden: d_n = 1,748 \cdot \left(\ln(n_e)\right)^{0.63} \tag{2.39} Im Fall einer Häufigkeitsverteilung klassierter Messwerte ist \bar{x}_{0.95} = \bar{x}_k + \frac{n_e/2 - A_k}{a_k} \cdot \Delta x \quad \text{für} \quad A_k < \frac{n_e}{2} \quad \text{und} \tag{2.40} wobei x_{L_k} : \text{untere Grenze der k-ten Klasse} \Delta x : \text{Klassenbreite} a_k : \text{absolute Häufigkeit der Messwerte in der k-ten Klasse} A_k : \text{absolute Summenhäufigkeit der Messwerte bis zur unteren Grenze der k-ten Klasse} ``` Image Analysis: ### Image 1 Analysis #### Localization and Attribution: - **Numbering & Location:** There is only one image on the page, so it will be referred to as **Image 1**. #### Text Analysis: 1. **Mathematical Equations and Variables:** - Multiple equations are shown, including formulas for calculating statistical values such as span (R), maximum and minimum values (\(x_{max}, x_{min}\)), and the correction factor (k). - An equation for \( k = \frac{6}{d_n} \) (2.38) is used considering the sample size. - The formula \(d_n = 1.748 - (\ln(n_e))^{0.663}\) (2.39) is given for expected values when \(n_e > 20\). 2. **Content and Significance:** - Descriptions and mathematical derivations are given to assist in statistical analysis, specifically focusing on sample ranges (\(x_{max}, x_{min}\)), and corrections. - Formulae are tailored to aid in understanding the expected values distribution in statistical samples and aid in their adjustments. 3. **Table of Expected Values:** - **Table Title:** Erwartungswert der w-Verteilung in Abhängigkeit von \(n_e\). - **Columns:** - \(n_e\): representing the effective sample size. - \(d_n\): denoting the expected value for the w-distribution. - **Data Points in Table:** - \( n_e = 20, d_n = 3.74 \) - \( n_e = 25, d_n = 3.93 \) - \( n_e = 30, d_n = 4.09 \) - \( n_e = 35, d_n = 4.21 \) - \( n_e = 40, d_n = 4.32 \) - \( n_e = 45, d_n = 4.42 \) - \( n_e = 50, d_n = 4.50 \) #### Table Analysis: 1. **Data Points:** - The table clearly lists effective sample sizes \(n_e\) alongside their corresponding expected values \(d_n\). - **Insight:** The table demonstrates that as the effective sample size (\(n_e\)) increases, the expected value (\(d_n\)) also increases. 2. **Formula Application:** - For samples larger than \(n_e > 20\), the expected value \( d_n \) can be recalculated using the provided logarithmic formula. ### Additional Notes: - The document appears to be a technical or scientific text, possibly a manual or a statistical reference, providing detailed formulae and tables for statistical analysis. - The page label 'Seite 17' and 'VW 101 30: 2005-02' suggests it's from a technical or academic publication, indicating a systematic and highly detailed approach typical of such documents. ### Perspective and Composition: - **Perspective:** The perspective is a straightforward, document-style capture of a page, likely from a textbook or an academic paper. - **Composition:** The page is neatly organized with sections clearly delineated by numbers, equations, and tables. ### Contextual Significance: - This image appears to be part of a larger document focused on providing detailed statistical and mathematical information. Its well-structured format aims to aid readers in understanding and applying statistical methodologies. ### Trend and Interpretation: - **Trend:** The presented analyses suggest a systematic increase in expected values with increasing sample size, a common trend in statistical sampling and analysis. - **Interpretation:** The data and equations provided help in precise modeling and calculation, essential for accurate statistical analysis and decision-making. #################### File: VW%2010130_DE%281%29.pdf Page: 18 Context: ``` ## 3.3 Grenzwerte zur Maschinenfähigkeit Zur Erlangung der Maschinenfähigkeit für ein betrachtetes Merkmal müssen die ermittelten Fähigkeitsschätzungen folgende Forderung bezüglich festgelegter Grenzwerte \( c_{\text{max},\text{grenz}} \) und \( c_{\text{min},\text{grenz}} \) erfüllen: - **zweiseitig toleriertes Merkmal:** \[ \hat{c}_{\text{max}} \geq c_{\text{max},\text{grenz}} \quad \text{und} \quad \hat{c}_{\text{min}} \geq c_{\text{min},\text{grenz}} \tag{3.1} \] - **einseitig toleriertes Merkmal** (7): \[ \hat{c}_{\text{max}} \geq c_{\text{max},\text{grenz}} \tag{3.2} \] bei einem effektiven Stichprobenumfang von \( n_e \geq 50 \). Sofern nichts anderes vereinbart, gelten folgende Fähigkeitsschätzwerte: \[ c_{\text{max},\text{grenz}} = 2,0 \] \[ c_{\text{min},\text{grenz}} = 1,67 \] In Fällen, in denen unter vertretbarem Aufwand nur eine Untersuchung mit einem kleineren effektiven Stichprobenumfang als 50 möglich ist, muss der daraus folgenden größeren Unsicherheit der ermittelten Fähigkeitsschätzwerte durch entsprechend größere Grenzwerte wie folgt Rechnung getragen werden. Die Ermittlung der Grenzwerte für effektive Stichprobenumfänge kleiner als 50 wird dabei auf die Grenzwerte bezogen, die sich aus der Forderung (3.1) oder (3.2) für die zu untersuchende Grundgesamtheit mit 95%-iger Wahrscheinlichkeit einhalten lassen (unter Vertrauensbereichsgrenzen). Diese ergeben sich unter der Annahme einer normalverteilten Grundgesamtheit aus der oberen Vertrauensbereichsgrenze der Standardabweichung \[ \sigma_s = \frac{\hat{c} - \bar{c}}{\sqrt{\frac{2}{n_e}}} \tag{3.3} \] und dem statistischen Anteilebereich für die Fertigungsstreuung \[ X_{90.965\%} \quad \text{bis} \quad X_{10.135\%} = \bar{c} \pm t_{0.965\%} \cdot \frac{1 + 1}{2 \cdot 50} \cdot \frac{49}{2 \cdot 5.49} \tag{3.4} \] wobei \[ t_{0.965\%} = 3,0: \quad \text{Quantil der standardisierten Normalverteilung} \] \[ \chi^2_{0.965\%} = 33,93: \quad \text{Quantil der Chi-Quadrat-Verteilung bei einem Freiheitsgrad von} \quad f = 49 \quad \text{(siehe auch [1])} ``` Image Analysis: 1. **Localization and Attribution:** - There is one image on the page, which I will refer to as Image 1. 2. **Object Detection and Classification:** - Image 1 contains text. 4. **Text Analysis:** - The text in Image 1 is in German and consists of a section from a document discussing the limits for machine capability. This includes mathematical formulas and conditions for determining capability indexes (\(c_{m,\text{Grenz}}\) and \(c_{mk,\text{Grenz}}\)). - The text is structured as follows: - Section header 3.3: "Grenzwerte zur Maschinenfähigkeit" ("Limits for Machine Capability"). - Several formulas for different types of capability measures (e.g., for two-sided and one-sided toleranced characteristics). - Conditions for the sample sizes and required capability indices if not otherwise agreed upon (\(c_{m,\text{Grenz}} = 2.0\) and \(c_{mk,\text{Grenz}} = 1.67\)). - Descriptions of the statistical basis for calculating these values, including quantiles from the normal distribution (\(U_{99.865\%} = 3.0\)) and chi-square distribution (\(\chi_{49;2.5\%}^2 = 33.9\)). 8. **Color Analysis:** - The document is primarily black and white with different sections possibly highlighted using bold text and underlining for emphasis. 9. **Perspective and Composition:** - The image is a photographed or scanned single-page document from a manual or technical report. The text is structured into sections with subsections and formulas dispersed throughout. 10. **Contextual Significance:** - This image appears to be part of a technical guideline or standard, possibly for quality assurance in manufacturing. The detailed text and formulas are intended to set guidelines for assessing and maintaining machine capability. 11. **Metadata Analysis:** - The only metadata visible in the image is the document identifier "VW 101 30: 2005-02", suggesting it might be related to Volkswagen or a similar organization’s standard documentation. ### Summary: Image 1 contains detailed text from a technical document discussing thresholds for machine capability, including formulas and conditions for evaluating capability indices. The document appears to establish certain statistical measures and standards necessary for consistent quality control in manufacturing processes. #################### File: VW%2010130_DE%281%29.pdf Page: 19 Context: Durch Umformen und Einsetzen in die Auswerteformeln (2.1) und (2.2) ergeben sich daraus die Fähigkeitengrenzwerte für die Grundgesamtheit \[ c_m \geq c_{m,\text{grenz}} \; = \; 0,832 \cdot c_{m,\text{grenz}} \tag{3.5} \] \[ c_m \geq c_{m,\text{grenz}} \; = \; 0,824 \cdot c_{m,\text{grenz}} \tag{3.6} \] Somit ergeben sich für effektive Stichprobengrößen \(n_e < 50\) folgende angepasste Fähigkeitengrenzwerte: \[ c_m \geq c_{m,\text{grenz}} \; = \; 0,832 \cdot \sqrt{\frac{f}{2 \cdot t_k}} \tag{3.7} \] \[ \hat{c}_{mk} \geq c_{m,k,\text{grenz}} \; = \; 0,824 \cdot \left(1 + \frac{1}{2 - n_e} \right) \cdot \sqrt{\frac{f}{2 \cdot t_{k}}} \tag{3.8} \] mit dem Freiheitsgrad \[ f = n_e - 1 \tag{3.9} \] ### Beispiel: Bei festgelegten Fähigkeitengrenzwerten von \(c_{m,\text{grenz}} = 2,0\), \(c_{m,k,\text{grenz}} = 1,67\) und einem effektiven Stichprobenumfang von \(n_e = 20\) ergeben sich nach den Formeln (3.7) bis (3.9) die folgenden angepassten Grenzwerte für ein zweistellig toleriertes Merkmal: \[ \hat{c}_m \geq 2,0 \cdot 0,832 \cdot \sqrt{\frac{20-1}{10,1}} = 2,28 \] \[ \hat{c}_{mk} \geq 1,67 \cdot 0,824 \cdot \left(1 + \frac{1}{2 - 20} \right) \cdot \sqrt{\frac{20 - 1}{10,1}} = 1,93 \] \* Die Ermittlung der angepassten Fähigkeitengrenzwerte mit Hilfe der Formen (4.7) bis (4.9) wird nicht für nicht normalverteilte Grundgesamtheiten verwendet, da es für diese zur Zeit keine anderen Methoden gibt und damit zumindest eine brauchbare Berücksichtigung eines Stichprobenumfangs erfolgt, der kleiner als 50 ist. Image Analysis: ### Analysis of the Provided Visual Content: **Page Identification:** - This is a single page (Seite 19) from a document identified as "VW 101 30; 2005-02". ### 1. Localization and Attribution: - This document consists of a single image, so it is denoted as **Image 1**. ### 2. Object Detection and Classification: - **Image 1** contains textual content. - Key objects: Text, equations, and a footnote. ### 3. Scene and Activity Analysis: - **Scene Description:** The document appears to be a technical or engineering document, discussing mathematical formulations. - **Main Activities:** The scene involves the explanation and calculation of capability indices and associated limits based on different formulas. ### 4. Text Analysis: #### Upper Section: - **German Text:** - "Durch Umformen und Einsetzen in die Auswerteformeln (2.1) und (2.2)..." translates to "By rearranging and substituting into the evaluation formulas (2.1) and (2.2)..." - The section explains how specific capability limits for the basic population are derived. - **Equations:** - Several mathematical formulas are displayed, labeled, and referenced in the text: - Equation (3.5) to (3.9) provide calculations for capability indices \(C_m\) and \(C_{mk}\) along with the confidence intervals for small sample sizes. - **Example Calculation:** - Provides a process for calculating adjusted capability indices for a sample size \(n_e = 20\): - \( \hat{C}_m \geq 2.0 \times 0.832 - \sqrt{\frac{20 - 1}{10 \cdot 1}} = 2.28 \) - \( \hat{C}_{mk} \geq 1.67 \times 0.824 \left(1 + \frac{1}{2 \cdot 20}\right) - \sqrt{\frac{20 - 1}{10 \cdot 1}} = 1.93 \) #### Footnote: - The footnote clarifies the use of adjusted capability limit values using Formulas 4.7 and 4.9. It states that these should not be used for normally distributed basic populations nor generalized methods but are suitable for smaller sample counts less than 50. ### 7. Anomaly Detection: - There is no anomaly detected in this text or the formulas. The content appears to be typical for a mathematical or technical standard document. ### 9. Perspective and Composition: - **Perspective:** Top-down view, traditional text document style. - **Composition:** The page is composed of blocks of text, formulas, and footnotes. Formulas are paired with textual explanations. ### 10. Contextual Significance: - The content likely forms part of a larger technical manual or standard for evaluating process capabilities and quality control metrics. - This page contributes to understanding how to adjust capability indices for different sample sizes, a crucial aspect in quality engineering. ### 11. Metadata Analysis: - There is no visible metadata. There isn't any mention of dates, camera settings, or specific digital information beyond the document identification. ### 13. Graph Numbers: - No graphical data points are present; the information is strictly in text and formula format. ### Additional Aspects: **Ablaufprozesse und Prozessbeschreibungen (Process Flows and Descriptions):** - The document extracts describe processes for calculating and adjusting capability indices. **Typen Bezeichnung (Type Designations):** - Refers to different types of capability indices (\(C_m\), \(C_{mk}\)). **Trend and Interpretation:** - The main trend is the adjustment of capability indices for smaller sample sizes. This indicates adapting standard quality control metrics for different contexts. **Tables:** - There are no tables present. This document serves as a technical reference for engineers or quality control specialists working on process capability and related metrics. #################### File: VW%2010130_DE%281%29.pdf Page: 20 Context: # 3.4 Statistische Tests Die Messwerte einer Maschinenfähigkeitsuntersuchung dürfen in der Regel keine - unerwartet große Abweichung einzelner Messwerte (Ausreißer) gegenüber der Streuung der anderen Messwerte, - signifikante Änderung der Fertigungshäufigkeiten während der Stichprobenentnahme und - signifikante Abweichung vom erwarteten Verteilungsmodell aufweisen. Andernfalls ist mit zusätzlichen systematischen Einflüssen auf die Fertigung zu rechnen. Für dieses Verhalten sollten dann die Ursachen bekannt und deren Wirkung akzeptabel sein, um die Voraussetzungen eines sicheren Fertigungsprozesses zu erfüllen. Zur Überprüfung der oben genannten Kriterien sind daher bei einer Maschinenfähigkeitsuntersuchung entsprechende statistische Tests anzuwenden. Da diese Tests in Normen und Standardwerken der Statistikliteratur ausführlich beschrieben sind, werden sie im Folgenden nur mit Verweisen angegeben: Folgende Tests sind im Rahmen einer Maschinenfähigkeitsuntersuchung durchzuführen: - **Test auf Ausreißer** mittels verlustunabhängigen Test nach Hampel in modifizierter Form (siehe VW 10133) - **Test auf Änderung der Fertigungsgüte** mittels verlustunabhängigem Run-Test nach Swed-Eisenhärd (siehe [1]) - **Test auf Abweichung von der Normalverteilung** nach Epps-Pulley (siehe ISO 5479) - **Test auf Abweichung von einem beliebigen festgelegten Verteilungsmodell** mittels Chi-Quadrat-Test (siehe [1]) Die statistischen Tests laufen alle nach dem folgenden Schema ab: 1. **Aufstellen der Nullhypothese** \( H_0 \) und der Alternativhypothese \( H_1 \) - \( H_0 \): Die Grundsamtheit der Messwerte des betrachteten Merkmals ist nicht normalverteil - \( H_1 \): Die Grundsamtheit der Messwerte des betrachteten Merkmals ist normalverteilt 2. **Festlegen der Aussagewahrscheinlichkeit** \( \alpha = 1 - \beta \) oder Irrtumswahrscheinlichkeit \( \alpha \) 3. **Aufstellen der Form für die Prüfgröße** 4. **Berechnen des Prüfwertes** aus den Stichprobenwerten nach der Prüfgröße/Senorformel 5. **Ermitteln des Schwellenwertes** der Testverteilung 6. **Vergleich des Prüfwertes mit dem Schwellenwert zur Entscheidung**, ob ein Widerspruch zur Nullhypothese vorliegt und damit die Alternativhypothese gilt Zu beachten ist, dass bei einem statistischen Test mit der angegebenen Aussagewahrscheinlichkeit \( \alpha \) gegebenenfalls nur ein Mittelanspruch zur Nullhypothese nachgewiesen werden kann, z.B. dass eine signifikante Abweichung der Messwerte von einer normalverteilten Grundsamtheit vorliegt. Ergibt sich aus dem Testergebnis kein Widerspruch zur Nullhypothese, so ist dies keine Bestätigung der Gültigkeit der Nullhypothese. Es lässt sich also in diesem Fall mit der gegen einen Aussagewahrscheinlichkeitswert \( \alpha \) nicht nachweisen, dass eine normalverteilte Grundsamtheit nicht vorliegt. Man entscheidet sich dann in Analogie zum Rechtssprinzip \( 2 \) im Zweifelsfall für den Angeklagten" lediglich für die Annahme der Nullhypothese. Durch die Irrtumswahrscheinlichkeit \( \alpha \) wird das Risiko angegeben, aufgrund des Testergebnisses die Nullhypothese zu verwerfen, obwohl sie zutrifft (\( \alpha\)-Risiko). Für die Irrtumswahrscheinlichkeit kann nun aber nicht einfach eine beliebig kleine „Wert“ festgelegt werden, denn dadurch würde z.B. das Risiko steigen, eine tatsächliche Abweichung von einer Normalverteilung nicht zu entdecken (\( \beta \)-Risiko). Image Analysis: ### Comprehensive Examination of the Visual Content #### Localization and Attribution: - **Document Layout:** - The page contains a single image, positioned centrally on the page. - The image will be referred to as **Image 1** for this analysis. #### Text Analysis: - **Text Content:** - The document appears to be a technical manual or study, written in German. - The section referenced is **3.4 Statistische Tests** (Statistical Tests). - **Page Number:** Seite 20 - **Document Identification:** VW 101 30: 2005-02 - **Main Content Analysis:** - The text discusses statistical tests used in the context of machine capability investigations. - Key points include: - Avoidance of unexpected large deviations of individual measurements. - Significant changes in production quality during sampling phases. - Significant deviations from the expected distribution model. - Types of statistical tests mentioned: - **Test auf Ausreißer** - Test for outliers using Hampel's modified method. Reference: [VW 10133]. - **Test auf Änderung der Fertigungslage** - Test for changes in production position using the Run-Test by Swed-Eisenhart. - **Test auf Abweichung von der Normalverteilung** - Test for deviation from normal distribution using the Epps-Pulley test. Reference: [ISO 5479]. - **Test auf Abweichung von einem beliebig festgelegten Verteilungsmodell** - Test for deviation from a predefined distribution model using Chi-square test. - **Testing Methodology:** - Establishing null hypothesis (H0) and alternative hypothesis (H1). - Determining significance level (γ = 1 - α or error probability α). - Formulating the test statistic. - Extracting the test value from sample data to determine the level of confidence or decision-making threshold. - **Risk Analysis:** - **Alpha Risk (α-Risiko):** Probability of erroneously rejecting the null hypothesis. - **Beta Risk (β-Risiko):** Failing to detect a deviation from normal distribution. #### Contextual Significance: - **Document Context:** - The document appears to be a technical manual or guideline, likely related to quality control or engineering processes. - It focuses on statistical methodologies to analyze and ensure machine capability and production consistency. #### Process Descriptions: - **Statistical Test Process:** - Descriptions include the step-by-step process for conducting various statistical tests to ensure production quality and detect deviations or outliers. #### Typen Bezeichnung: - **Type Designations:** - Different types of statistical tests are designated, specifying the methodologies used and their applicable standards or references. ### Conclusion: The document is a technical guideline on statistical tests pertinent to machine capability investigations, providing detailed descriptions of the test types, methodologies, and associated risks. The content is highly focused on precision and reliability in production, emphasizing the importance of statistical validation in quality control processes. #################### File: VW%2010130_DE%281%29.pdf Page: 21 Context: # 4 Durchführung einer Maschinenfähigkeitsuntersuchung Eine Maschinenfähigkeitsuntersuchung (MFU) ist nach dem in den Bildern 9 bis 11 dargestellten Ablauf durchzuführen. ``` Start |-- 4.1 Prüfmittelanwendung |-- 4.2 Stichprobenentnahme |-- Bedingungen zur MFU erfüllt? |-- ja --> 4.3 Sonderregelung für eingeschränkte MFU |-- nein |-- 4.4 Datenauswertung |-- 4.5 Dokumentation |-- 4.6 Ergebnisbeurteilung |-- Auswertungswiederholung? |-- ja --> 4.7 Maschinenoptimierung |-- nein |-- Maschine fähig? |-- ja --> machbare Maschinenoptimierung |-- nein --> 4.8 Behandlung nicht fähiger Maschinen ``` **Ende** ![Bild 9 - Ablauf einer Maschinenfähigkeitsuntersuchung](link-zum-bild) Image Analysis: ### Comprehensive Examination of the Visual Content **Image 1 - Process Flowchart** #### **Localization and Attribution:** - This is the only image on the page, hence it is designated as Image 1. #### **Diagram and Chart Analysis:** - **Flowchart Analysis:** - This flowchart depicts a procedure titled "Durchführung einer Maschinenfähigkeitsuntersuchung" which translates to "Conducting a Machine Capability Study." - The flowchart starts with an oval labeled "Start" at the top. - It then branches out into different rectangles representing different steps and diamonds illustrating decision points. - **Key Components:** 1. **4.1 Prüffmittelanwendung** - (Use of test equipment) 2. **4.2 Stichprobenentnahme** - (Sampling) 3. **Bedingungen zur MFU erfüllt** - (Conditions for MFU met) - If conditions are met (ja/yes): - **4.4 Datenauswertung** - (Data evaluation) - **4.5 Dokumentation** - (Documentation) - **4.6 Ergebnisbeurteilung** - (Result assessment) - Decision diamond splits into: - **Auswertungswiederholung** - (Evaluation repeat) - If machinery is capable (ja/yes) -> leads to "Ende" (End) - If machinery isn't capable (nein/no) -> leads to **4.7 Maschinenoptimierung** - (Machine optimization) - Decision diamond for further machinery improvement: - If further improvement is possible (ja/yes) -> loop back to **4.7 Maschinenoptimierung** - If not (nein/no) -> leads to **4.8 Behandlung nicht fähiger Maschinen** - (Treatment of incapable machines) - If conditions are not met (nein/no): - **4.3 Sonderregelung für eingeschränkte MFU** - (Special regulation for limited MFU) - Then it follows the same flow forward. #### **Text Analysis:** - The text primarily includes German terms used in a manufacturing or quality control context. - **Header Information:** - "Seite 21 VW 101 30: 2005-02" at the top right specifies the page number and a document reference code. - **Title:** - "Durchführung einer Maschinenfähigkeitsuntersuchung" translates to "Conducting a Machine Capability Study." - **Content Description:** - "Eine Maschinenfähigkeitsuntersuchung (MFU) ist nach dem in den Bildern 9 bis 11 dargestellten Ablauf durchzuführen." - This statement explains that a machine capability study (MFU) must be conducted according to the sequence shown in images 9 to 11. - **Footnote:** - "Bild 9 - Ablauf einer Maschinenfähigkeitsuntersuchung" translates to "Figure 9 - Procedure of a Machine Capability Study." #### **Ablaufprozesse (Process Flows):** - The flowchart shows a step-by-step process to conduct an MFU, detailing various stages such as the application of test equipment, sampling, data evaluation, documentation, result assessment, and decisions regarding machine optimization or treatment of incapable machines. - The flow is logical and guides the user through different scenarios based on conditions being met or not met, and whether the machine is capable or not. #### **Prozessbeschreibungen (Process Descriptions):** - Step **4.1**: Use of test equipment. - Step **4.2**: Sampling. - Step **4.3**: Special regulation for limited MFU if conditions aren't met. - Step **4.4**: Data evaluation. - Step **4.5**: Documentation. - Step **4.6**: Result assessment. - Step **4.7**: Machine optimization if it’s not capable and optimization is possible. - Step **4.8**: Treatment of incapable machines if further optimization isn’t feasible. #### **Typen Bezeichnung (Type Designations):** - Identifies various steps (like data evaluation, documentation, etc.) and decisions (like machinery optimization). #### **Trend and Interpretation:** - If the machine conditions are favorable, the process moves towards data evaluation, documentation, and result assessment leading to regular operation if all conditions are satisfied. - If machine conditions are unfavorable, special regulations or machine optimization procedures are followed, indicating a structured approach to handle different scenarios. #### **Perspective and Composition:** - The flowchart is a classic top-down procedural diagram, making it easy to follow the sequence of steps from start to end. This detailed analysis offers insight into the methodical approach presented for conducting a machine capability study, helping in understanding the importance of evaluating and optimizing industrial machinery processes. #################### File: VW%2010130_DE%281%29.pdf Page: 22 Context: # 4.4 Datenauswertung ## 4.4.1 Auswahl des zu erwartenden Verteilungsmodells ## 4.4.2 Test auf Ausreißer ### Ausreißer vorhanden? - **ja** - 4.4.3 Ausreißer aus der Berechnung der statistischen Kennwerte nehmen - **nein** - 4.4.4 Test auf Änderung der Fertigungslage - 4.4.5 Test auf Abweichung vom festgelegten Verteilungsmodell ### Abweichung vom Verteilungsmodell? - **ja** - 4.4.8 Verteilungsfreie Auswertung - **nein** - Normalverteilung? - **ja** - 4.4.6 Auswertung nach Normalverteilung - 4.4.7 Auswertung nach festgelegtem Modell - **nein** - Fortsetzung in 4 ![Bild 10 - Ablauf der Datenauswertung](image-url-here) Image Analysis: ### Image Analysis Report #### Localization and Attribution - **Image Number**: Image 1 (Starting from the top of the page). #### Diagram and Chart Analysis - **Diagram Type**: Flowchart - **Title**: Bild 10 - Ablauf der Datenauswertung (Figure 10 - Data Evaluation Process). - **Page Info**: Page 22, VW 101 30: 2005-02 - **Description**: - The diagram represents a flowchart detailing the process of data evaluation. - The flowchart starts with "4.4 Datenauswertung" (4.4 Data Evaluation). #### Scene and Activity Analysis - **Entire Scene**: The image is a structured flowchart that lays out steps involved in a process. - **Major Activities**: - The flowchart illustrates steps sequentially with decision points affecting the flow. - Process begins with the selection of an expected distribution model. - Tests are conducted for outliers and potential changes in manufacturing conditions, followed by assessing deviations from the set distribution model and determining normal distribution. - Depending on the results of these tests, subsequent steps of evaluation are selected, either to a predefined model or a distribution-free evaluation. #### Text Analysis - **Detected Text**: - **Header**: Seite 22, VW 101 30: 2005-02 - **Main Process**: "4.4 Datenauswertung" (4.4 Data Evaluation). - **Sub-processes**: - "4.4.1 Auswahl des zu erwartenden Verteilungsmodells" (4.4.1 Selecting the expected distribution model). - "4.4.2 Test auf Ausreißer" (4.4.2 Test for outliers). - Further steps include handling outliers, changes in manufacturing conditions, deviations from distribution models, and opting for normal or distribution-free evaluation. - **Significance**: The text provides a clear and systematic procedure for data analysis, indicating specific steps and decisions to be made at each point in the process. #### Anomaly Detection - **Observation**: There are no noticeable anomalies or unusual elements in the diagram. The flowchart is logically structured and easy to follow. #### Color Analysis - **Color Composition**: The flowchart is monochromatic, primarily using black lines and text on a white background. - **Impact**: The use of monochrome allows for clear readability and focus on the content without distractions from colors. #### Perspective and Composition - **Perspective**: The image is a straightforward 2D flowchart. - **Composition**: The flowchart is well-organized, with a top-to-bottom hierarchical structure, providing a straightforward flow of information and decision points using standard flowchart symbols (ovals for process start/stop, diamonds for decision points, rectangles for process steps). #### Ablaufprozesse (Process Flows) - **Process Described**: Detailed process for data evaluation, involving several steps and decision points, ensuring thorough analysis and handling of data. - **Significance**: Ensures systematic analysis, identification, and handling of anomalies, enhancing data reliability and integrity in manufacturing or statistical evaluations. #### Typen Bezeichnung (Type Designations) - **Types and Categories**: Steps in the data evaluation process, such as testing for outliers or choosing evaluation models, defined by their process number (e.g., 4.4.1, 4.4.2, etc.). ### Conclusion This flowchart (Image 1) methodically details the evaluation process of data. It addresses decision points, the approach for handling outliers, changes in manufacturing conditions, and the adoption of relevant distribution models, ensuring a comprehensive and methodical process for data assessment. The absence of color and anomalies supports the professional and clear presentation of the significant technical process. #################### File: VW%2010130_DE%281%29.pdf Page: 23 Context: # 4.6 Ergebnisbeurteilung - Ausreißer vorhanden - ja - Ausreißer durch fehlerhafte Messungen - nein - Änderung der Fertigungslage - ja - nein - Abweichung vom Verteilungsmodell - ja - anderes Verteilungsmodell möglich - ja - Auswertungswiedertholung - Fortsetzung in 4 - nein - Ursache bekannt und Wirkung akzeptabel - ja - Fähigkeitskennwerte kleiner als Grenzwerte - ja - Maschine fähig - Fortsetzung in 4 - nein - Maschine nicht fähig - Fortsetzung in 4 - nein Image Analysis: ### Image Analysis #### Localization and Attribution: 1. **Image Identification and Numbering**: - This is the only image on the page, thus it is denoted as **Image 1**. #### Object Detection and Classification: 2. **Object Detection**: - The main object in the image is a flowchart, which consists of various shapes such as diamonds, ovals, and rectangles. - There are arrows connecting these shapes, indicating the direction of the process flow. #### Scene and Activity Analysis: 3. **Scene Description**: - The scene depicts a flowchart detailing a specific process titled "4.6 Ergebnisbeurteilung" (Result Evaluation). - The activities captured in the flowchart involve decision-making steps that lead to different outcomes based on various conditions. #### Text Analysis: 4. **Text Extraction and Analysis**: - The text in the flowchart includes numerous German terms and a few specific phrases: - "4.6 Ergebnisbeurteilung" (Result Evaluation) - This is the title and indicates the subject of the flowchart. - "Ausreißer vorhanden" (Outliers present) - "Änderung der Fertigungslage" (Change in production situation) - "Abweichung vom Verteilungsmodell" (Deviation from distribution model) - "Fähigkeitskennunwerte kleiner als Grenzwerte" (Capability values less than limits) - "Ursache bekannt und Wirkung akzeptabel" (Cause known and effect acceptable) - "Ausreißer durch fehlerhafte Messungen" (Outliers due to faulty measurements) - "Maschine fähig" (Machine capable) - "Maschine nicht fähig" (Machine not capable) 5. **Significance in Context**: - These terms indicate a step-by-step process to evaluate results, considering different factors and conditions to determine the capability of a machine within a production setting. #### Diagram and Chart Analysis: 6. **Diagram Analysis**: - The chart presents a process flow for result evaluation. It includes a number of decision points (diamonds) and actions (rectangles and ovals). - The diagram's flow is from top to bottom, moving from one decision/action to another based on the conditions met. 7. **Process Flow Description**: - The process begins with checking for outliers. If no outliers are present, it proceeds directly to evaluating machine capability. - If outliers are present, it checks if they're due to faulty measurements. If yes, it stops; if no, it proceeds to evaluate the production situation and potential deviations from the model. - Depending on these evaluations, it determines if the machine is capable or not, requiring repeats or acceptances based on known causes and acceptable effects. #### Typen Bezeichnung (Type Designations): 8. **Type Designations**: - Types are specified within the flowchart, indicating different decision points and actions attributed to them. Examples include "Ja" (Yes) and "Nein" (No) as decisions leading to specific processes. ### Summary: - **Image 1** is a flowchart diagram explaining the steps for result evaluation in a production setting, specifically focusing on the detection and treatment of outliers, production changes, model deviations, and machine capability. The flowchart uses various symbols to indicate decision points and actions, guiding the user through a logical sequence based on set conditions. Key elements include dealing with outliers, evaluating distribution models, and determining machine capability, significant to ensuring accurate production results. #################### File: VW%2010130_DE%281%29.pdf Page: 24 Context: # 4.1 Prüfmittelanwendung Zur MFU ist nur ein Prüfmittel anzuwenden, das von der zuständigen Stelle für den vorgesehenen Prüfprozess freigegeben wurde. # 4.2 Stichprobenentnahme Eine MFU bezieht sich auf ein Fertigungsmerkmal oder einen Maschinenparameter. In der Regel sind zur Auswertung die einzelnen Messwerte der Stichprobe zu erfassen. Im Fall von manuell aufgezeichneten Messwerten in Form von Strichen in einer Klasseneinteilung des Wertereinheits (Stichliste) kann statt dessen auch die Häufigkeitsverteilung der klassierten Messwerte erfasst werden. Um bei einer MFU im Wesentlichen nur den Maschineninfluss zu erfassen, sind folgende Bedingungen bei der Fertigung der Stichproben zu einhalten: - Eine einheitliche **Rohteilcharge** und eine einheitliche **Vorbereitung** (Lieferant, Werkstoff) muss bei der Untersuchung gewährleistet sein. Während der MFU ist die Maschine oder Anlage immer vom gleichen Bediener zu fahren. - Die **Vorbereitungsqualität** der zu beiliefernden Merkmale muss den geforderten Fertigungsvorschriften entsprechen. - Die Anzahl der gefertigten Teile (**Stichprobenumfang**) sollte in der Regel 50 betragen. Ist dieser Stichprobenumfang aus wirtschaftlichen oder technischen Gründen schwer realisierbar, so ist auch ein kleinerer zulässig. Zu beachten sind dann entsprechend größere Grenzwerte nach Tabelle 3 oder den Formen (3.7) und (3.8). Der effektive Stichprobenumfang (d.h. ohne Ausreißer) muss aber mindestens 20 betragen. - Die Teile sind unmittelbar hintereinander zu fertigen und der **Fertigungshäufigkeit** entsprechend zu nummerieren. An jedem Teil sind alle festgelegten Merkmale zu untersuchen. - Die MFU darf nur bei **betriebswarmer Maschine** erfolgen. **Betriebswarm** ist für jeden Anwendungsfall zu definieren. - Die Prüfpflichten sind unter den für die Maschine geforderten **Serienbedingungen** (d.h. mit der Taktzeit und den Maschineninflussparametern der Serienfertigung) zu fertigen. Entsprechend dem Projekt müssen spezielle Festlegungen getroffen werden, damit zu Beginn der MFU gewährleistet ist, dass z.B. das **Werkzeug** eingebaut ist und dass Ende der Werkzeugnutzungszeit nicht innerhalb der MFU liegt. - **Werkzeugwechsel**, manuelle Werkzeugverstellungen oder sonstige Änderungen von Maschinenparametern dürfen während der MFU nicht vorgenommen werden. Ausgenommen davon sind automatische Werkzeugrückführungen durch integrierte Steuerungen. - Bei **Maschinenstörungen** während der MFU, die das untersuchte Merkmal beeinflussen, muss mit der MFU neu begonnen werden. - Die **Messmittel** müssen vor der Untersuchung gefertigt und zwischen Lieferant und Abnehmer abgestimmt sein. - Bei der Fertigung unterschiedlicher Teile (einschließlich Teilunumfänge, z.B. B. Stahlblech/Gussteile) auf einer Maschine, die außerdem verschiedene Merkmale aufweisen können, sind für alle diese Teile MFUs durchzuführen. Image Analysis: **Image Analysis:** 1. **Localization and Attribution:** - **Image Position:** The provided image occupies a single page, containing one image. - **Image Number:** Image 1. 2. **Text Analysis:** - The image contains a document written in German. - **Content:** - **Section 4.1:** Prüfrnittelanwendung (Test Equipment Application) - Explanation on the necessity for the MFU to use only approved testing equipment. - **Section 4.2:** Stichprobenentnahme (Sampling) - Detailed guidelines on how sampling should be conducted for variability tests, highlighting factors like uniform raw materials, preparation quality, number of samples, requirement for operating conditions, and machine-specific parameters. - **Significance:** This document seems to be part of a procedural manual or guidelines related to quality control or production standards in a manufacturing setting. The content outlines critical steps and considerations for ensuring that tests and samples are taken consistently and effectively to capture the true quality and performance of the produced items. 3. **Contextual Significance:** - **Overall Document Theme:** The image represents a page from a technical or procedural document, most likely associated with manufacturing, quality control, or industrial processes. - **Contribution to the Message:** - The detailed guidelines and requirements detailed in sections 4.1 and 4.2 emphasize the importance of standardization and consistency in testing and production processes. - Highlight the necessary conditions and quality measures to be observed to ensure reliable and accurate production assessments. 4. **Color Analysis:** - The document is primarily in black and white, which is typical for formal procedural documentation, ensuring that the information is clear and focused without visual distractions. - **Impact:** The use of black text on a white background ensures maximum readability and clarity. 5. **Perspective and Composition:** - **Perspective:** The image appears to be a scan or a direct capture of a page from a document, taken from a straight, overhead view. - **Composition:** The text is organized into structured sections with numbered headings (4.1 and 4.2), subsections, and bullet points, which make it easy to follow and extract specific information. 6. **Anomaly Detection:** - There are no apparent anomalies. The document appears standard, without irregularities. 7. **Ablaufprozesse (Process Flows):** - Discusses processes like sampling, preparation quality, ensuring machine-specific parameters, and defining operational states. - **Significance:** These processes are crucial for maintaining and verifying the consistency and quality of production batches. 8. **Prozessbeschreibungen (Process Descriptions):** - Detailed descriptions include how the sampling should be done, what parameters should be maintained, and precautions during the testing procedure. - **Typen Bezeichnung (Type Designations):** - May refer to terms like "Rohteilcharge" (batch of raw parts), "Prüfteile" (test parts), and "Betriebswarmen Maschine" (operationally warm machine). **Summary:** This document page is highly specialized, providing structured guidelines for conducting sample testing and ensuring quality control in a manufacturing or production environment. The emphasis on detailed procedural steps indicates the importance of maintaining strict standards and consistency in the manufacturing process. #################### File: VW%2010130_DE%281%29.pdf Page: 25 Context: # 4.3 Sonderregelung für eingeschränkte MFU Lassen sich die in 4.2 genannten Bedingungen zur Stichprobennahme nicht vollständig erfüllen, so kann in begründeten Fällen eine eingeschränkte MFU durchgeführt werden, für die Sonderregelungen zwischen Lieferanten und Abnehmer zu vereinbaren sind und unter dem Vermerk „Eingeschränkte MFU“ zu dokumentieren sind. # 4.4 Datenauswertung ## 4.4.1 Auswahl des zu erwartenden Verteilungsmodells Das zu erwartende Verteilungsmodell hängt von der Merkmalsart ab. Für die wichtigsten Arten von Merkmalen (siehe auch VW 01056) sind die zugeordneten Verteilungsmodelle aus Tabelle 2 zu entnehmen. | Merkmalsart | Verteilungsmodell | |------------------------------|-------------------| | Längenmaß | N | | Durchmesser, Radius | N | | Geradheit | B1 | | Ebenheit | B1 | | Rundheit | B1 | | Zylinderform | B1 | | Linienform | B1 | | Flächenform | B1 | | Parallelität | B1 | | Rechtwinkligkeit | B1 | | Neigung (Winkligkeit) | B1 | | Position | B2 | | Koaxialität / Konzentrizität | B2 | | Symmetrie | B1 | | Rundlauf | B2 | | Planlauf | B2 | | Rauheit | B1 | | Unwucht | B2 | | Drehmoment | N | **Legende:** N: Normalverteilung B1: Betragsverteilung 1. Art B2: Betragsverteilung 2. Art (Rayleigh-Verteilung) Für nicht aufgeführte Merkmalsarten kann in den meisten Fällen eine Zuordnung einer Verteilung nach der folgenden Regel erfolgen: - bei zweiseitiger oder einseitiger nach unten tolerierten Merkmalen eine Normalverteilung - und bei einseitig nach oben tolerierten Merkmalen eine Betragsverteilung 1. oder 2. Art Image Analysis: ### Comprehensive Examination of the Provided Visual Content **Localization and Attribution:** - There is a single page to analyze, containing one image. Hence, it will be referred to as **Image 1**. #### Image 1 Analysis: **Text Analysis:** 1. **Heading and Subheadings:** - **"4.3 Sonderregelung für eingeschränkte MFU"** - Special regulation for limited MFU. - **"4.4 Datenauswertung"** - Data Analysis. - **"4.4.1 Auswahl des zu erwartenden Verteilungsmodells"** - Selection of the expected distribution model. 2. **Main Text:** - **4.3:** This section indicates that if the conditions mentioned in section 4.2 for random sampling are not fully met, a limited MFU (Measurement for Uncertainty) can be conducted. This requires agreement between suppliers and customers and needs to be documented under the note "Eingeschränkte MFU." - **4.4.1:** This section explains that the selected distribution model depends on the type of feature. The distribution models for the most critical types of features (as per VW 01056) are provided in Table 2. 3. **Table 2 - Zuordnung von Merkmalsarten und Verteilungsmodellen (Assignment of Feature Types and Distribution Models):** - This table categorizes various feature types and assigns corresponding distribution models: - **Längenmaße:** Length measures - Normalverteilung (N) - **Durchmesser, Radius:** Diameter, radius - Normalverteilung (N) - **Geradheit:** Straightness - Betragsverteilung 1. Art (B1) - **Ebenheit:** Flatness - B1 - **Rundheit:** Roundness - B1 - **Zylinderform:** Cylindrical shape - B1 - **Linienform:** Line form - B1 - Additional attributes such as **Flächenform**, **Parallelität**, etc. with corresponding distribution models B1, B2, or N. 4. **Legende (Legend):** - **N:** Normalverteilung (Normal distribution) - **B1:** Betragsverteilung 1. Art (Distribution of the 1st type) - **B2:** Betragsverteilung 2. Art (Rayleigh distribution). 5. **Footnotes:** - Provides details on scenarios where features not listed can follow either normal distribution (N) or distribution type 1 or 2 based on the given rules. **Diagram and Chart Analysis:** - **Table 2:** This table is a key aspect containing a list of feature types and their corresponding distribution models. It is structured with feature types on the left and their distribution models on the right. - **Trends and Insights:** The table showcases the different distribution models based on the feature types, predominantly using normal and first-type distributions, with a smaller portion utilizing second-type distribution. **Prozessbeschreibungen (Process Descriptions):** - The text on the page delineates the process for selecting distribution models based on feature types. It highlights the importance of document agreements for certain deviations in sampling conditions and provides a systematic approach to categorize these feature types with appropriate distribution models. **Trend and Interpretation:** - A clear trend in the table is that many geometric and structural characteristics (e.g., straightness, flatness, roundness) align with the first-type distribution model (B1), suggesting a preference or norm for this method in process quality management. - The selection criteria for features not listed indicate a flexible, yet controlled approach to data analysis and measurement uncertainty. The presented information provides a structured approach to managing and documenting measurement uncertainties and distribution models for different feature types in quality management processes. #################### File: VW%2010130_DE%281%29.pdf Page: 26 Context: ``` ## 4.4.2 Test auf Ausreißer Mit Hilfe des verlustunabhängigen AusreißerTests nach VW 10133 ist zunächst zu ermitteln, ob die erfassten Messwerte Ausreißer enthalten. Ausreißer sind Messwerte, die so weit von den anderen Messwerten entfernt liegen, dass sie mit hoher Wahrscheinlichkeit nicht aus derselben Grundgesamtheit stammen wie die übrigen Werte, wie z.B. fehlerhafte Messungen. Der AusreißerTest ist mit einer Aussagewahrscheinlichkeit von 99% durchzuführen. ### 4.4.3 Ausreißer aus der Berechnung der statistischen Kennwerte nehmen Im Fall identifizierter Ausreißer werden diese bei der Berechnung der statistischen Kennwerte nicht berücksichtigt. Die Ausreißer dürfen aber nicht gelöscht werden. Sondern sie sind in der grafischen Darstellung des Einzelverlaufes entsprechend zu kennzeichnen, und ihre Anzahl ist in der Dokumentation anzugeben. ### 4.4.4 Test auf Änderung der Fertigungstiefe Mit Hilfe des verlustunabhängigen Run-Tests nach Swed-Eisenhardt (siehe [1]) ist zu ermitteln, ob sich die Fertigungstiefe während der Stichprobenahme systematisch geändert hat. Die systematische Änderung der Fertigungstiefe kann z.B. durch Temperaturunterschiede oder durch werkzeugspezifischen Trendverlauf (Trendverlauf). Dieser Test ist mit einer Aussagewahrscheinlichkeit von 95% durchzuführen. Falls nur die Häufigkeitsverteilung klassierter Messwerte erfasst wurde, lässt sich dieser Test nicht anwenden. ### 4.4.5 Test auf Abweichung vom festgelegten Verteilungsmodell Die erfassten Messwerte sind zu prüfen, ob sie eine signifikante Abweichung von dem Verteilungsmodell aufweisen, das für das betreffende Merkmal festgelegt wurde. Dazu ist im Fall einer festgelegten Normalverteilung der Epps-Pulley-Test (siehe ISO 5479) und im Fall eines anderen festgelegten Verteilungsmodells, z.B. bei einer Belastungsverteilung 1. oder 2. Art, der Chi-Quadrat-Test (siehe [1]) mit einer Aussagewahrscheinlichkeit von 95% anzuwenden. Eine Abweichung vom festgelegten Verteilungsmodell kann z.B. durch unterschiedliche Materialienberger der Stichprobenahme entstehen (Mischverteilung, siehe Beispiel 1 in Abschnitt 5). Eine Abweichung vom festgelegten Verteilungsmodell kann z.B. durch Stichprobenentnahmen von verschiedenen Werkzeugen entstehen (Mischverteilung, siehe auch Beispiel 3, in Abschnitt 5). ### 4.4.6 Auswertung nach Normalverteilung Im Fall einer festgelegten oder einer nach den Kriterien (1.13), (1.22) größeren Normalverteilung, in dem die Messwerte keine signifikante Abweichung vom Verteilungsmodell aufweisen, erfolgt die Berechnung der Fähigkeitskennwerte nach der Tolerierung nach den Formen (2.1) bis (2.5), wobei die Streuungsgrenzen nach (2.6) ermittelt werden. ### 4.4.7 Auswertung nach festgelegtem Modell Im Fall eines festgelegten Verteilungsmodells, z.B. Betragsermittlung 1. oder 2. Art, in dem die Messwerte keine signifikante Abweichung vom Verteilungsmodell aufweisen, erfolgt die Berechnung der Fähigkeitskennwerte nach den Formen (2.1) bis (2.5), wobei die Kenwerte der einzuspeisenden Verteilung nach den Formen (2.15) und (2.16) bzw. (2.24) und (2.25) mit Hilfe der genäherden Funktion (2.18) bzw. (2.27) ermittelt und die Streuungsgrenzen nach den genäherden Funktionen (2.19) bzw. (2.22) berechnet werden können. ``` Image Analysis: **Text Analysis:** 1. **Image 1:** - **Text Detected:** - **Title:** Test auf Ausreißer - **Sections:** - 4.4.2 Test auf Ausreißer - 4.4.3 Ausreißer aus der Berechnung der statistischen Kennwerte nehmen - 4.4.4 Test auf Änderung der Fertigungslage - 4.4.5 Test auf Abweichung vom festgelegten Verteilungsmodell - 4.4.6 Auswertung nach Normalverteilung - 4.4.7 Auswertung nach festgelegtem Modell **Content Analysis & Significance:** - **4.4.2 Test auf Ausreißer:** Provides guidelines on how to conduct an outlier test using VW 10133 standard, specifying that extreme values should be removed if they deviate significantly from other measurements. The test aims to ensure a 99% confidence level in identifying outliers. - **4.4.3 Ausreißer aus der Berechnung der statistischen Kennwerte nehmen:** Discusses removing identified outliers from statistical calculations. Instead of deleting them, outliers should be marked and documented. - **4.4.4 Test auf Änderung der Fertigungslage:** Details the method to detect systematic changes in production position using Swed-Eisenhard run tests, ensuring a 95% probability of detecting significant changes due to factors like temperature or tool wear. - **4.4.5 Test auf Abweichung vom festgelegten Verteilungsmodell:** Describes the procedure to assess if measurements significantly deviate from the defined distribution model, using tests like the Epps-Pulley test or Chi-square test, with a 95% confidence level. Examples of misdistribution are provided in Section 5. - **4.4.6 Auswertung nach Normalverteilung:** Outlines the evaluation process when there's a significant deviation from normal distribution using specific formulas (2.1) to (2.5) based on tolerance and capability indicators. - **4.4.7 Auswertung nach festgelegtem Modell:** Explains the evaluation following a set distribution model using defined formulas to measure capability indicators and calculation limits, ensuring proper assessment protocols. **Contextual Significance:** - This document page is part of a larger technical manual or standard, specifically VW 101 30: 2005-02, section 4.4, related to quality control and statistical methods for production processes. The text ensures precision and accuracy in manufacturing by outlining standardized test procedures for identifying and handling data outliers and deviations. This contributes to maintaining high-quality production standards by providing structured methods to detect and address anomalies in measurements and processes. #################### File: VW%2010130_DE%281%29.pdf Page: 27 Context: 4.4.8 Verteilungsfreie Auswertung --------------------------- Ergibt sich aus dem statistischen Test ein Widerspruch zwischen den erfassten Messwerten und dem festgelegten Verteilungsmodell, oder lässt sich zum betrachteten Fertigungsmerkmal kein passendes Verteilungsmodell finden, so erfolgt eine verteilungsfreie Berechnung der Fähigkeitskennnwerte nach den Formeln (2.29) bis (2.40). 4.5 Dokumentation ---------------- Die Dokumentation einer MFU bezüglich eines Merkmals muss folgende Informationen und Darstellungen enthalten: ### Kopfdaten: - Abteilung, Bearbeiter und Erstellungsdatum - Angaben über das Teil - Benennung, Nennmaß und Toleranz des Merkmals - Maschinenangaben - Prüfmittelangaben - Zeitraum der Fertigung ### Ergebnisse: - Grafische Darstellung des Einzelwerteverlaufs mit den Stichprobenmittelwerten mit Grenzlinien des Toleranzintervalls (sofern Einzelwerte erfasst wurden) - Histogramm mit dem eingepassten Verteilungsmodell, Grenzlinien des Toleranzintervalls und Streubereichs, sowie Mittelwert- bzw. Medianwertlinie - Darstellung in Wahrscheinlichkeitsnetz mit dem eingepassten Verteilungsmodell, Grenzlinien des Toleranzintervalls und Streubereichs, sowie Mittelwert- bzw. Medianwertlinie (siehe [2]) - Anzahl der gemessenen Werte - Anzahl der ausgewerteten Messwerte oder gefundenen Ausreißer - Schätzwerte der Fertigungslage - Schätzwerte der Streubreitegrenzen oder Schätzwert der Streubreite - Das angewandte Verteilungsmodell - Das Ergebnis des Tests auf Änderung der Fertigungslage - Das Ergebnis des Tests auf Abweichung vom festgelegten Verteilungsmodell - Berechnete Fähigkeitskennwerte für Cm und Cmk (auf zwei Stellen nach dem Komma) - Geforderte Grenzwerte für Cm und Cmk ### Hinweise und Bemerkungen: - Gegebenenfalls Hinweis auf eingeschränkte MFU - Gegebenenfalls besondere Vereinbarungen zwischen Lieferanten und Abnehmer - Gegebenenfalls besondere Ereignisse während der Stichprobenahme Image Analysis: ### Text Analysis #### Image 1 1. **Localization and Attribution:** - The image is located centrally. - It is labeled as **Image 1**. 2. **Text Analysis:** - **Section Titles and Subsections:** - The text is a snippet from a document detailing procedures and evaluations related to "Verteilungsfreie Auswertung" (Distribution-Free Evaluation) and "Dokumentation" (Documentation). - Main sections are labeled as **4.4.8 Verteilungsfreie Auswertung** and **4.5 Dokumentation**. - "Seite 27 VW 101 30: 2005-02" indicates it is page 27 of a VW (Volkswagen) procedural document from 2005, version 02. - **Main Content Summary:** - **4.4.8 Verteilungsfreie Auswertung:** Discusses the statistical test for determining consistency between measured values and a distribution model. If no suitable distribution model is found, capability values are calculated using specific formulas (2.29 and 2.40). - **4.5 Dokumentation:** Outlines required information and representations for documenting a test feature, including: - **Header Data:** Department, editor, creation date, part information, naming, nominal size, tolerance of feature, machine details, test equipment, and production period. - **Results:** Graphical representation of individual value progression, histograms, distribution models, number of measured values, outliers, capability indices (Cm, Cmk), and specific agreements during sampling. ### Scene and Activity Analysis - The scene appears to be a scanned or digitally captured page from a corporate procedural document. - There are no active scenes or visible activities as it is text-based documentation. ### Object Detection and Classification - The image contains only text and is classified under documents or written materials. ### Contextual Significance - The documentation appears to be directed towards quality assurance and statistical evaluation in a manufacturing or production setting within the automobile industry. - It serves as a guide for documenting and evaluating test features of production components, ensuring compliance with specified tolerances and statistical models. ### Conclusion - **Key Insight:** This document page is part of a procedural manual providing guidelines for statistical evaluation and documentation of test features in production, emphasizing the importance of accurate and detailed documentation to ensure quality control in manufacturing processes. #################### File: VW%2010130_DE%281%29.pdf Page: 28 Context: # 4.6 Ergebnisauswertung Ob eine Maschine bezüglich der Fertigung eines betrachteten Merkmals als fähig bewertet werden kann, hängt von der folgenden Ergebnisauswertung ab: Ergebnis bei einer Auswertung \( c_{\text{ausreißer}} \) ist deren Ursache zu klären. Ausreißer dürfen nur durch fehlerhafte Messverfahren verursacht werden oder durch den Ausreißer selbst, aufgrund der festgelegten Toleranzschwellen nicht fähig zu beurteilen. Werden mehr als 5 % der ersten Messwerte dafür mehr als 2 Werte als Ausreißer identifiziert, dann ist zu untersuchen, ob der Prüfprozess fehlerhaft ist. Die MFU ist dann gegebenenfalls zu wiederholen. Hat sich die **Fertigungseigenschaft** während der Stichprobenahme signifikant geändert, so muss in der Regel deren Ursache bekannt und deren Wirkung akzeptabel sein, um die Voraussetzung zur Maschinenfähigkeit zu erfüllen (Annahme siehe letzten Absatz des Abschnitts). Liegt eine **einheitliche Ausreißerverteilung** vor und lässt sich kein anderes Verteilungsmodell den betrachteten Merkmalen widerspruchsfrei zuordnen, so muss die Ursache bekannt und die Wirkung akzeptabel sein. Sofern nichts anderes vereinbart, müssen die ermittelten Fähigkeitskennwerte bei einem effektiven Stichprobenumfang von \( n_{s} \geq 50 \) (d.h. ohne Ausreißer) die Forderung \[ \hat{c}_{mk} \geq 2,20 \quad \text{und} \quad \hat{c}_{mk} \geq 1,67 \] für ein zweifelsfrei toleriertes Merkmal \[ c_{mk} \geq 1,67 \] für ein einseitig toleriertes Merkmal erfüllen, um die Maschinen als fähig beurteilen zu können. Dabei sind zum Vergleich mit den Grenzwerten die ermittelten Fähigkeitskennwerte auf zwei Stellen nach dem Komma zu runden, so dass z.B. ein ermittelter Wert von \( \hat{c}_{mk} = 1,665415 \) mit der sich daraus ergebenen Rundung von 1,67 die Forderung noch erfüllt. Bei einem effektiven Stichprobenumfang \( 20 \leq n_{s} < 50 \) sind entsprechend größere Grenzwerte einzuhalten. Für einige Stichprobenumfänge sind in Tabelle 3 die angepassten Grenzwerte angegeben. Bei Vereinbarung anderer Grenzwerte auf der Basis von \( n_{s} \geq 50 \) sind die entsprechenden angepassten Grenzwerte nach Formel (3.7) bis (3.9) zu ermitteln. ## Tabelle 3 - Grenzwerte zur Maschinenfähigkeit für \( 20 \leq n_{s} < 50 \) | \( n_{s} \) | \( \hat{c}_{mk} \) | \( c_{mk} \) | |-------------|-------------------|---------------| | 20 | 2,28 | 1,93 | | 25 | 2,19 | 1,85 | | 30 | 2,13 | 1,79 | | 35 | 2,08 | 1,75 | | 40 | 2,05 | 1,72 | | 45 | 2,02 | 1,70 | | 50 | 2,00 | 1,67 | Ergibt sich ein Fähigkeitskennwert, der kleiner ist als der entsprechende Grenzwert, dann ist die Maschine als nicht fähig zu beurteilen. Image Analysis: ### Image Analysis #### 1. Localization and Attribution - **Image:** Single image. - Located centrally on the page. #### 2. Object Detection and Classification - **Objects Detected:** - Text blocks. - Table (Tabelle 3). #### 3. Scene and Activity Analysis - **Scene Description:** - The image seems to be a scanned document page or a screenshot of a textual document. - The text is primarily in German and discusses criteria for evaluating machine production capabilities. #### 4. Text Analysis - **Text Detected:** - Main Header: "4.6 Ergebnisbeurteilung" - Sub-headers and paragraphs discussing various aspects of evaluating machine production features and their tolerances. - Mathematical symbols and formulas indicating statistical values and acceptance criteria. - **Key Text Elements and Their Significance:** - The document part is about "Ergebnisbeurteilung" which translates to "Result Evaluation." - It details how to determine if a machine can be considered capable concerning a particular production feature. - Discusses conditions under which deviations (Ausreißer) must be addressed. - Contains formulas critical for determining machine capability indexes (Cm and Cmk). - References the consistency and adjustment of tolerance limits. - Contains a table (Tabelle 3) listing the thresholds for capability indices for different sample sizes. #### 5. Diagram and Chart Analysis - **Table Analysis:** - **Table Content:** Tabelle 3 shows the "Grenzwerte zur Maschinenfähigkeit" (Threshold values for machine capability) for sample sizes from 20 to 50. - **Columns:** - \( n_0 \) - Sample size. - \( \bar{C}_m \) and \( \bar{C}_{mk}^2 \) - represent different capability indices. - **Data Points:** - 20: 2.28, 1.93 - 25: 2.19, 1.85 - 30: 2.13, 1.79 - 35: 2.08, 1.75 - 40: 2.05, 1.72 - 45: 2.02, 1.70 - 50: 2.00, 1.67 - **Trend and Interpretation:** - The table displays decreasing values for capability indices as the sample size increases. - Indicates tightening tolerance and increased scrutiny with larger sample sizes. #### 6. Product Analysis - Not Applicable (NA). #### 7. Anomaly Detection - **Possible Anomalies:** - NA. #### 8. Color Analysis - **Color Composition:** - Predominantly black and white. - Standard format for a document scan or screenshot of a text-based document. #### 9. Perspective and Composition - **Perspective:** - The image is taken from a direct, front-facing view commonly used for document digitization. - **Composition:** - Text is structured and organized into headings, paragraphs, and a table. #### 10. Contextual Significance - **Context:** - This section is likely part of a larger technical or quality manual, addressing processes and criteria for machine capability evaluations in a manufacturing context. - **Contribution:** - Provides specific guidelines and numerical thresholds crucial for the technical assessment of machinery. - Ensures consistency and standardization in production quality assessments. ### Summary The analyzed image is a document page from a technical manual discussing criteria for machine capability evaluation. It outlines conditions under which machines are evaluated, introduces statistical formulas, and provides a critical table of threshold values for different sample sizes to ensure production quality. The analysis centers around this structured text and numerical data that help in determining machine capabilities in a manufacturing setup. #################### File: VW%2010130_DE%281%29.pdf Page: 29 Context: 4.7 Maschinenoptimierung Für den Fall, dass die Maschinenfähigkeit bezüglich des untersuchten Merkmals nicht nachgewiesen werden konnte, sind Maßnahmen zur Maschinenoptimierung erforderlich. Dazu sind die entsprechend Einfluss nehmenden Faktoren zu identifizieren (z. B. mittels statistischer Versuchs-methodik (DOE)) und zu beseitigen. 4.8 Behandlung nicht fähiger Maschinen Lässt sich die Maschinenfähigkeit mit wirtschaftlich vertretbaren Maschinenoptimierungen nicht erreichen, so sollte zunächst mit Hilfe der statistischen Toleranzenrechnung nach VW 01057 untersucht werden, ob eine Toleranzerweiterung zur Erreichung der Maschinenfähigkeit möglich ist. Ist auch durch diese Maßnahmen keine Maschinenfähigkeit zu erreichen, so ist zu entscheiden, ob die Maschine nach schriftlich vereinbarten Sonderregelungen abgenommen wird oder nicht. Diese Sonderregelungen sollten folgende Punkte enthalten: - Begründungen für die Abnahme - Risiko- und Kostenbetrachtungen - gegebenenfalls einschränkende Fertigungs- und zusätzliche Prüfbedingungen - Angabe der Verantwortlichkeit Image Analysis: ### Image Analysis **Localization and Attribution:** - **Position Identification:** - This document appears to be a single-page text document. - No images are present on this page. ### Text Analysis: - **Detected Text:** - Main Text Sections: - **Heading:** - "Maschinenoptimierung" (4.7) - "Behandlung nicht fähiger Maschinen" (4.8) - **Body Text:** - "Bei einem ermittelten Fähigkeitskennwert c_mk ≥ 2,33 ..." - "Für den Fall, dass die Maschinenfähigkeit bezüglich des untersuchten Merkmals nicht nachgewiesen werden konnte, sind Maßnahmen zur Maschinenoptimierung erforderlich..." - "Lässt sich die Maschinenfähigkeit mit wirtschaftlich vertretbaren Maschinenoptimierungen nicht erreichen, so sollte zunächst..." - Subpoints under “Behandlung nicht fähiger Maschinen” include: - Begründungen für die Abnahme - Risiko- und Kostenbetrachtungen - gegebenenfalls einschränkende Fertigungs- und zusätzliche Prüfbedingungen - Angabe der Verantwortung - **Text Analysis:** - The text pertains to machine optimization and dealing with machines that do not meet capability requirements. - Section 4.7 outlines steps for machine optimization if the machine capability could not be demonstrated. - Section 4.8 details steps to address non-capable machines when optimization is economically unfeasible, suggesting statistical tolerance adjustments and other economic considerations. - Points to consider when accepting machines with special arrangements include justification for acceptance, risk and cost considerations, potential restrictive manufacturing conditions, and specifying responsibility. ### Color Analysis: - **Dominant Colors:** - The document is primarily black and white. - The text is black on a white background, maintaining high contrast and readability. ### Perspective and Composition: - **Perspective:** - The document is presented in a standard block text format typical of technical documents and instructions. - **Composition:** - The layout is straightforward, with headings, numbered sections, and bullet points to organize information efficiently. - The headings are clearly defined in bold, making it easy to discern different sections at a glance. ### Contextual Significance: - **Overall Document Context:** - The document is part of a technical instruction manual or specification guide likely dealing with machine operational standards and optimization protocols. - **Contribution to Message:** - The text contributes to the overall message by providing detailed guidelines and procedures for ensuring machine capability and steps to take when machines do not meet required standards. ### Tables and Diagrams: - **Presence:** - None are present in the provided page. ### Process Flow (Ablaufprozesse): - **Described Processes:** - The process for determining machine capability and subsequent optimization steps if initial capability is not demonstrated. - The process for managing machines that are not capability-compliant, including tolerance adjustments and special agreement approvals. ### Trend and Interpretation: - **Trends:** - Emphasis on systematic evaluation and optimization of machine capabilities. - Consideration of economic feasibility and pragmatic solutions when direct optimization is not viable. ### Summary: The document provides detailed procedural guidance on machine optimization and handling non-capability machines, emphasizing statistical methods, economic considerations, and clear responsibility delineation. The structured composition enhances clarity, making it a practical reference for technical personnel in manufacturing or quality assurance roles. #################### File: VW%2010130_DE%281%29.pdf Page: 30 Context: ``` # 5 Beispiele ## Beispiel 1: Wellenburchmesser mit einem Nennmaß von 20 mm, einem Mindestmaß von \( G_L = 19.7 \, \text{mm} \) und einem Höchstmaß von \( G_H = 20.3 \, \text{mm} \) Aus den \( n = 50 \) Messwerten der Stichprobe ergeben sich durch die statistischen Tests keine Ausreißer, keine signifikante Lageänderung und keine signifikante Abweichung von einer zu erwartenden Normalverteilung. Es wurden folgende Stichprobenkenngrößen ermittelt: - \( \bar{x} = 20.05 \, \text{mm} \) - \( s = 0.05 \) Es ergeben sich daher nach Formel (2.11) aus den Stichprobenkenngrößen die folgenden Schätzerwerte der Streubreitegrenzen für die normalverteilte Grundgesamtheit: - \( x_{0.135} = \bar{x} - 3 - 0.05 \, \text{mm} = 19.99 \, \text{mm} \) - \( x_{99.865} = \bar{x} + 3 + 0.05 \, \text{mm} = 20.21 \, \text{mm} \) und daraus ergeben sich schließlich die folgenden Fähigkeitskenngrößen: - \( C_m = \frac{G_H - G_L}{x_{99.865} - x_{0.135}} = \frac{20.3 - 19.7}{20.2 - 19.99} = 2.0 \) - \( C_{mk} = \min \left( \frac{G_H - \bar{x}}{ \bar{x} - x_{0.135}}, \frac{G_L - \bar{x}}{x_{99.865} - \bar{x}} \right) = \min \left( \frac{20.3 - 20.05}{20.2 - 20.05}, \frac{19.7 - 20.05}{20.21 - 20.05} \right) = \min \left( \frac{0.25}{0.15}, \frac{-0.35}{0.16} \right) = 1.67 \) Durch die ermittelten Fähigkeitskenngrößen wird somit nachgewiesen, dass die Maschine bezüglich des betrachteten Wellenburchmessers die Fähigkeitsanforderungen gerade noch erfüllt. ![Bild 12 - Beispiel einer Fertigung mit dem Modell einer Normalverteilung und den Fähigkeitskennwerten \( C_m = 2.0 \) und \( C_{mk} = 1.67 \)](Bild12) ``` Image Analysis: ### Comprehensive Examination of the Attached Visual Content #### 1. Localization and Attribution - **Image Location and Numbers:** - There is a single image on the page. - It is numbered as **Image 1**. #### 2. Object Detection and Classification - **Image 1:** - Objects present: Bar graph with overlaid normal distribution curve, labelled axes, reference lines, and data points. #### 4. Text Analysis - **Text Extraction:** - The document contains several blocks of German text explaining a statistical example. - Key textual elements extracted: - "Beispiel 1:" introduces the example. - Detailed calculations of statistical limits and capability indices. - Labels and descriptions for the graph such as "Bild 12 - Beispiel einer Fertigung mit dem Modell einer Normalverteilung und den Fähigkeitskennwerten 𝑐_𝑚 = 2,0 und 𝑐_𝑚𝑘 = 1,67." - **Text Content Significance:** - The text provides a detailed explanation of a capability study for a manufacturing process involving shaft diameters. - Descriptions include statistical calculations and figures, leading up to the interpretation of a normal distribution graph. #### 5. Diagram and Chart Analysis - **Image 1:** - **Axes and Scales:** - X-axis: Labeled "Messwert" (measurement value), ranging approximately from 19.70 to 20.30. - Y-axis: Labeled "Häufigkeit" (frequency), symbolizing the count or frequency of measurements. - **Legends and Labels:** - G_u = 19.7 - 𝑥₀.₀₁₃₅% = 19.9 mm - μ = 20.05 mm - 𝑥₉₉.₈₆₅% = 20.2 mm - G_o = 20.3 - **Key Insights:** - The graph visually represents the distribution of shaft measurements around a mean (μ) of 20.05 with labels indicating the specific percentile points (𝑥₀.₀₁₃₅% and 𝑥₉₉.₈₆₅%). - The capability indices 𝑐_𝑚 and 𝑐_𝑚𝑘 calculated (2.0 and 1.67 respectively) suggest that the process capability barely meets the specified quality requirements. #### 6. Product Analysis - **Image 1:** - Products depicted: Shaft measurement values. - Features: The key feature being measured is the diameter of the shafts, which are represented in terms of measurement values. #### 8. Color Analysis - **Image 1:** - The image is primarily composed of black and white. - The graph features a grey-shaded histogram overlaid by a black normal distribution curve, depicting the normal distribution of the data. #### 9. Perspective and Composition - **Image 1:** - The image is composed in a clear and straightforward manner, with the histogram centred on the page and overlaid by a normal distribution curve. - The text and labels are strategically placed around the graph to enhance readability and comprehension. #### 13. Graph Numbers - **Image 1:** - Not specific numerical data points listed in detail on the graph that require extraction line-by-line. - Data points and values for capability indices and percentiles are summarized in the annotations around the graph. #### Additional Aspects: - **Typen Bezeichnung (Type Designations):** - References to types such as 𝑐_𝑚 (Process Capability Index) and 𝑐_𝑚𝑘 (Corrected Process Capability Index) are present, demonstrating the specific measures used to evaluate the process capability. #### Contextual Significance - **Image 1:** - The image serves as a visual illustration of the statistical analysis results discussed in the text. - It enhances the reader's understanding of the process capability by visualizing the distribution of measurements. #### Trend and Interpretation - **Image 1:** - Clear visual representation of a normal distribution with process capability indices indicating that the machine just meets the capability requirements. Overall, the combination of textual explanations and graphical representation effectively communicates the statistical analysis of the manufacturing process to the reader. #################### File: VW%2010130_DE%281%29.pdf Page: 31 Context: # Beispiel 2 Bohrung mit einer maximal zulässigen Positionsabweichung von \( G_0 = 0,2 \, \text{mm} \). Aus den n = 50 Messwerten der Stichprobe ergaben sich durch die statistischen Tests keine Ausreißer, keine signifikanten Lageänderungen und keine signifikante Abweichung von einer zu erwartenden Betragsverteilung. Es wurden folgende Stichprobenkennwerte ermittelt: \[ \mu = 0,038 \, \text{mm} \quad \text{und} \quad \sigma = 0,02 \, \text{mm} \] Aus den Stichprobenkennwerten ergibt sich das Verhältnis: \[ \frac{\mu}{\sigma} = \frac{0,038}{0,02} = 1,9 \] Da dieser Wert aufgrund der Zufallsstreuung der Stichprobenkennwerte kleiner als der Grenzwert 1,9131 nach Bedingung (2.23) ist, wird das Verhältnis auf diesen Grenzwert gesetzt, woraus sich wiederum eine Exzentrizität von \( z = 0 \) ergibt. Damit lässt sich der zweite Parameterwert der angepassten Betragsverteilung 2. Art nach dem Sonderfall (2.26) wie folgt berechnen: \[ \sigma_{1.3395} = 1,526 \cdot \sigma = 1,526 \cdot 0,02 \, \text{mm} = 0,0305 \, \text{mm} \] Nach Formel (2.27) ergeben sich schließlich die Schätzwerte der Streubereichsgrenzen: \[ x_{9.8695} = 5,5485 - x_{10.1359} = 5,5485 - 0,02 = 5,5485 \, \text{und} \quad x_{10.1359} = 0,0773 - \sigma = 0,0773 - 0,02 \, \text{mm} = 0,0016 \, \text{mm} \] Nach den Formeln (2.3) und (2.4) ergeben sich schließlich die folgenden Fähigkeitskennwerte: \[ C_{mk} = \frac{x_{9.8695} - x_{10.1359}}{G_0} = \frac{0,111 - 0,0016}{0,2} = 1,83 \] \[ C_{mk} = \frac{G_0 - \mu}{\sigma} = \frac{0,2 - 0,038}{0,111 - 0,038} = 2,22 \] ![Bild 13 - Beispiel einer Fertigung mit dem Modell einer Betragsverteilung 2. Art und den Fähigkeitskennwerten \( C_{mk} = 1,83 \) und \( C_{mk} = 2,22 \)](reference_to_image) Durch den ermittelten Kennwert \( C_{mk} \) wird somit nachgewiesen, dass die Maschine bezüglich der Positionsabweichung einer Bohrung die Fähigkeitstagsforderung gut erfüllt. Für den Kennwert \( C_{mk} \) ergbit sich aber eine Information über die Fertigungslage, wobei der kleinere \( C_{mk} \) Wert angibt, dass dieser näher an der natürlichen Grenze Null liegt als am Höchstmaß. Image Analysis: ### Analysis of the Attached Visual Content #### 1. Localization and Attribution - **Image 1:** Positioned at the lower half of the page. - **Text Content:** Located at the upper half and bottom half surrounding the image. #### 2. Object Detection and Classification - **Image 1: Line Graph** - **Objects Detected:** - X-axis: Labeled "Messwert" (Measurement Value) - Y-axis: Labeled "Häufigkeit" (Frequency) - Curve depicting a distribution - **Key Features:** - A curve representing a probability distribution. - Specific points marked on the curve: \( x_{0.135} \), \( \mu \), and \( x_{99.865\%} \). - Annotations indicating specific values and areas of interest. #### 3. Scene and Activity Analysis - **Image 1:** - **Scene Description:** A line graph is presented. - **Activities:** The graph illustrates the results of a production process using a model of a certain type of distribution (2nd type). #### 4. Text Analysis - **Text Detected and Content:** - "Beispiel 2:" — Example 2 - "Bohrung mit einer maximal zulässigen Positionsabweichung von G₀ = 0,2 mm." — Drilling with a maximum permissible positional deviation of G₀ = 0.2 mm. - Several lines of calculations and explanations describing the statistical testing and results. - "Bild 13 veranschaulicht das Auswertergebnis" — Figure 13 illustrates the evaluation result. - "Bild 13 - Beispiel einer Fertigung mit dem Modell einer Betragsverteilung 2. Art und den Fähigkeitskennwerten ..." — Figure 13 - Example of manufacturing with the model of a 2nd type distribution and the capability indices \( C_m = 1.83 \) and \( \hat{C_{mk}} = 2.22 \). #### 5. Diagram and Chart Analysis - **Image 1: Line Graph** - **Axes and Scales:** - X-axis (Messwert): Range from 0.00 to 0.20 - Y-axis (Häufigkeit): No specific values marked on the graph. - **Data and Trends:** - The graph shows a bell-shaped curve representing the frequency of measurement values centered around a mean \( \mu \). - Points \( x_{0.135} \) and \( x_{99.865\%} \) represent specific values that likely denote bounds related to the distribution. #### 6. Product Analysis - **No products detected.** #### 7. Anomaly Detection - **No anomalies detected.** #### 8. Color Analysis - **Not applicable (greyscale document).** #### 9. Perspective and Composition - **Image 1:** - **Perspective:** Front-facing view of the graph. - **Composition:** The graph is centered horizontally on the page, with annotations and text above and below it providing context. #### 10. Contextual Significance - **Text and Graph Contribution:** - The text provides a detailed mathematical and statistical analysis of a drilling process with specific positional deviation constraints. - The graph illustrates the capability indices derived from the statistical model, reinforcing the theoretical explanations provided in the text. #### 11. Metadata Analysis - **None available from the screenshot.** #### 12. Graph and Trend Analysis - **Image 1:** - **Trends and Significance:** - The graph shows how the actual measurement values are distributed around a mean value, conforming to a certain type of distribution. - Capability indices \( C_m \) and \( \hat{C_{mk}} \) provide insights into the precision and reliability of the manufacturing process. #### 13. Graph Numbers - **Not applicable, no specific data points other than label values.** #### Additional Aspects - **Ablaufprozesse (Process Flows):** - The text describes a process pertaining to drilling and the statistical evaluation of the process accuracy. - **Prozessbeschreibungen (Process Descriptions):** - Detailed explanation of statistical methods used. - Calculations to determine process capability indices. - **Typen Bezeichnung (Type Designations):** - The document explicitly mentions a "2nd type of distribution" model. - **Trend and Interpretation:** - The trend indicates that the drilling process is statistically evaluated and meets the specified criteria. - \( C_m \) and \( \hat{C_{mk}} \) signify good process capability. - **Tables:** - None detected. Overall, this document provides a thorough statistical analysis of a drilling process's positional deviation and uses graphical representation to support the textual explanation. #################### File: VW%2010130_DE%281%29.pdf Page: 32 Context: # Seite 32 ## WV 101 30: 2005-02 ### Beispiel 3: Wellendurchmesser mit einem Nennmaß von 20 mm, einem Mindestmaß von \( G_L = 19,7 \, \text{mm} \) und einem Höchstmaß von \( G_S = 20,3 \, \text{mm} \). Aus den \( n = 50 \) Messerwerten der Stichprobe ergeben sich durch die statistischen Tests keine Ausreißer und keine signifikanten Lagenabweichungen, aber eine signifikante Abweichung von einer zu erwartenden Normalverteilung. Es erfolgt daher eine verteilungsfreie Auswertung nach Abschnitt 3.2.2. Dazu werden folgende Stichprobenkenngrößen ermittelt: \[ \bar{x} = \overline{x} = 20,202 \, \text{mm}, \quad x_{\max} = 20,199 \, \text{mm} \quad und \quad x_{\min} = 19,85 \, \text{mm} \] Korrekturfaktor nach Formel (2.38) und Tabelle 1: \[ k = \frac{6}{d_n} = \frac{6}{5} = 1,33 \] Spannweite nach Formel (2.37): \[ R = x_{\max} - x_{\min} = (20,19 - 19,85) \, \text{mm} = 0,34 \, \text{mm} \] Nach Formel (2.36): \[ x_c = \frac{x_{\max} + x_{\min}}{2} = \frac{20,19 + 19,85}{2} = 20,02 \, \text{mm} \] Schätzwerte für Streubreichsgrenzen nach Formel (2.35): \[ \hat{k}_0 = \bar{x} - k \frac{R}{2} = \left(20,02 - 1,33 \cdot \frac{0,34}{2}\right) \, \text{mm} = \frac{20,246}{19,794} \, \text{mm} \] Somit ergeben sich nach den Formeln (2.29) und (2.30) die Fähigkeitenkenngrößen: \[ \hat{c}_m = \frac{G_S - G_L}{\bar{x} - \hat{x}_u} = \frac{20,3 - 19,7}{20,246 - 19,794} = 1,33 \] \[ \hat{c}_{mk} = \min \left( \frac{G_S - \bar{x}}{\bar{x} - \hat{x}_u}, \frac{G_S - G_L}{\bar{x} - \hat{x}_{m}} \right) = \frac{20,3 - 20,02}{20,246 - 20,02} = 1,24 \] **Bild 14** - Beispiel einer Fertigung ohne definiertes Verteilungsmodell mit den Fähigkeitenkenngrößen \( c_m = 1,33 \) und \( c_{mk} = 1,24 \). Aus den ermittelten Fähigkeitenkennwerten ist zu entnehmen, dass die Maschine bezüglich des betrachteten Merkmals nicht die Fähigkeitenanforderung erfüllt. Ein interessanter Hinweis in diesem Zusammenhang liefert die signifikante Abweichung von einer erwarteten Normalverteilung. Denn damit wird Optimierungspotential erkennbar, wie hier im Fall einer Mischverteilung. Image Analysis: ### Image Localization and Attribution: - **Image Location**: The page contains a text block followed by a chart at the bottom. - **Image Numbering**: - **Image 1**: Text block containing equations and explanations. - **Image 2**: Bar chart. ### Object Detection and Classification: - **Image 1**: - **Objects**: Text, equations, numerical values. - **Category**: Mathematical/Engineering text and calculations. - **Image 2**: - **Objects**: Bar chart, axes, numerical values. - **Category**: Data visualization/chart. ### Scene and Activity Analysis: - **Image 1**: - **Scene**: The text describes a statistical analysis related to quality control in manufacturing. It includes formulas and calculated values. - **Activities**: Calculation, explanation of statistical methods, and quality assessment. - **Image 2**: - **Scene**: A bar chart visualizing frequency distribution. - **Activities**: Displaying and interpreting data related to quality metrics. ### Text Analysis: - **Image 1**: - **Extracted Text**: - The text describes an example of inspecting wave diameter, specifics of measurement such as mean, maximum, and minimum values. - Explanations include correction factors, span width, and various formulas to identify capability indices (e.g., \( \text{k}_0, \text{c}_{mk} \)). - **Significance**: This text is crucial for understanding the statistical methods and formulas used for determining process capability and how it applies to quality control. - **Image 2**: - **Extracted Text**: - Caption: “Bild 14 - Beispiel einer Fertigung ohne definiertes Verteilungsmodell mit den Fähigkeitskennwerten c_{\text{m}} = 1,33 und c_{\text{mk}} = 1,24” - **Significance**: This indicates an example manufacturing process with capability indices highlighting areas of improvement or deviation from expected distributions. ### Diagram and Chart Analysis: - **Image 2**: - **Axes**: - X-axis: Measurement values (Messwert) ranging from 19.7 to 20.3 mm. - Y-axis: Frequency (Häufigkeit), though the units are not clearly indicated. - **Legend/Labels**: The chart visualizes a histogram of measurement values with key markers (G_{\text{u}}, \(\bar{x}\), x_{30%}, x_{70%}, x_{0}). - **Data Trends**: The chart shows a skewed distribution of measurements, likely indicating a process deviation from normal distribution. ### Anomaly Detection: - **Image 2**: - **Unusual Elements**: The skew in the histogram suggests a potential issue in the manufacturing process, indicating process intervention may be necessary. ### Color Analysis: - **Image 2**: - **Color Composition**: Predominantly grayscale, with bars in a dark gray shade against a light gray background. - **Impact**: The monochrome color scheme focuses attention on the data without distractions, reinforcing the analytical nature of the content. ### Perspective and Composition: - **Image 2**: - **Perspective**: Front view, standard perspective for reading charts. - **Composition**: Centralized bar chart with labels and markers clearly identified, adhering to typical data representation standards for clarity. ### Contextual Significance: - **Overall Document Context**: The image and accompanying text contribute to a technical document, likely a manual or guideline for quality control in manufacturing, demonstrating how to apply statistical methods to assess and improve manufacturing processes. ### Graph and Trend Analysis: - **Image 2**: - **Trends**: The bar chart shows that most measurements fall within a certain range, but there is a significant tail, indicating non-normal distribution which might affect quality control processes. - **Significance**: This trend helps identify potential issues in the manufacturing process that require correction and highlights the importance of continuous process monitoring. ### Graph Numbers: - The histogram shows bars corresponding to measurement values ranging from: - 19.7 to 19.8 mm - 19.85 to 19.9 mm - 19.95 to 20.0 mm - 20.05 to 20.1 mm - 20.15 to 20.2 mm - 20.25 to 20.3 mm ### Tables: - **Image 1**: - **Table**: Contains calculated values such as mean (\(\bar{x}\)), correction factors, span width (R), and capability indices (\(c_m\) and \(c_{mk}\)). - **Content Description**: These values summarize the statistical assessment necessary for evaluating the capability of the manufacturing process. Overall, the images provide a detailed look into the application of statistical methods in evaluating and improving manufacturing processes. #################### File: VW%2010130_DE%281%29.pdf Page: 33 Context: # 6 Mitgelte Unterlagen - VW 010 56 Zeichnungen; Form- und Lagetoleranzen - VW 010 57 Statistische Toleranzrechnung von Maßketten - VW 101 33 Test auf Außerßer - DIN 55319 Qualitätsfähigkeitskenngrößen - ISO 5479 Statistical interpretation of data – Tests for departure from the normal distribution # 7 Literaturnhinweise [1] Graf, Henning; Stange, Willich, Formeln und Tabellen der angewandten mathematischen Statistik, Springer-Verlag, Dritte Auflage, 1987 [2] Kühlmeyer M., Statistische Auswertungsmethoden für Ingenieure, Springer-Verlag, 2001 Image Analysis: ### Image Analysis #### Localization and Attribution - **Image 1**: There is a single image present on the page. #### Text Analysis - **Detected Text**: **Section 6: Mitgeltende Unterlagen** - VW 010 56: Zeichnungen; Form- und Lagetoleranzen - VW 010 57: Statistische Toleranzrechnung von Maßketten - VW 101 33: Test auf Ausreißer - DIN 55319: Qualitätsfähigkeitskenngrößen - ISO 5479: Statistical interpretation of data – Tests for departure from the normal distribution **Section 7: Literaturhinweise** - [1] Graf, Henning, Stange, Wilrlich, Formeln und Tabellen der angewandten mathematischen Statistik, Springer-Verlag, Dritte Auflage, 1987 - [2] Kühlmeyer M., Statistische Auswertungsmethoden für Ingenieure, Springer-Verlag, 2001 - **Text Analysis and Significance**: - **Section 6: Mitgeltende Unterlagen**: This section lists relevant reference documents and standards. - **VW 010 56**: Relates to drawings and form and position tolerances, suggesting the importance of precision in measurements. - **VW 010 57**: Refers to statistical tolerance calculations of dimension chains, indicating the application of statistics in quality control. - **VW 101 33**: Pertains to the testing of outliers, likely in quality assessments. - **DIN 55319**: Discusses quality capability indices, which are crucial for determining the quality performance of processes. - **ISO 5479**: Focuses on statistical interpretation of data and tests for deviations from the normal distribution, which is essential for verifying process stability and capability. - **Section 7: Literaturhinweise**: Provides literature references. - **Reference [1]**: A book on formulas and tables used in applied mathematical statistics, useful for methodological and procedural reference. - **Reference [2]**: A book on statistical evaluation methods for engineers, essential for statistical analysis in engineering contexts. #### Contextual Significance - This image appears to be the 33rd page from a document titled "VW 101 30: 2005-02," suggesting it is part of a comprehensive standards or guidelines document used in an engineering or quality assurance context within the automotive industry (considering the use of "VW," likely referring to Volkswagen). #### Color Analysis - The image is predominantly composed of text in black on a white background which suggests a formal document and ensures readability and clarity. #### Perspective and Composition - The image is a direct scan or digital rendition of a document page. The text is centrally aligned with headings clearly demarcated in bold and sections numbered for easy navigation, indicating an organized and professional layout. ### No other aspects from the given list, including Object Detection and Classification, Scene and Activity Analysis, Diagram and Chart Analysis, Product Analysis, Anomaly Detection, Metadata Analysis, Graph and Trend Analysis, Graph Numbers, Ablaufprozesse, Prozessbeschreibungen, Typen Bezeichnung, Trend and Interpretation, or Tables, are applicable or present in this image. #################### File: VW%2010130_DE%281%29.pdf Page: 34 Context: # 8 Stichwortverzeichnis | Stichwort | Seite | Stichwort | Seite | |------------------------------------------------|-------|-------------------------------------|-------| | A | | I | | | absolute Häufigkeit a | 10 | Irrtumswahrscheinlichkeit α | 20 | | absolute Summenhäufigkeit A | 17 | K | 17 | | α-Risiko | 20 | Klassenbreite Δx | 17 | | Alternativhypothese | 20 | klassischer Messwerte | 10, 17| | angepasste Fähigkeitengrenzwerte | 19, 28| Korrekturfaktor k | 17 | | Ausreißer | 20, 26| L | | | Aussagewahrscheinlichkeit γ | 20, 26| Lage | 3 | | B | | M | | | Bedingungen zur MFU | 24 | Maschinenoptimierung | 29 | | β-Risiko | | Maschinenstörungen | 24 | | Betragsverteilung 1. Art | 5, 11 | Medianwert | 16 | | Betragsverteilung 2. Art | 7, 13 | Merkmalart | 4, 25 | | betriebswarme Maschine | 24 | Merkmalwert | 3 | | C | | Messmethode | 24 | | Capability | 3 | Mindestmaß Gu | 3, 9 | | Chiquadratl-Verteilung | 18 | Mischverteilung | 26, 32| | D | | Mittelwert μ | 4, 10 | | Datenauswertung | 25 | N | | | Dichtefunktion f(x) | 4 | Normalverteilung | 4, 10 | | Dokumentation | 27 | Nullhypothese | 20 | | E | | Nullpunktverschiebung | 6 | | eingeschränkte MFU | 25 | P | | | effektiver Stichprobenumfang nₑ | 10, 24| Parameter einer Verteilung | 3 | | Epps-Pulley-Test | 20, 26| Prüfgröße | 20 | | Ergebnisbeurteilung | 28 | Prüfwert | | | Erwartungswert der w-Verteilung dₙ | 17 | Prüfmittelanwendung | 24 | | Exzentristizität z | 7 | Q | | | F | | Quantil | 9 | | Fähigkeitsermittlung | 8 | - der standardisierten Normalverteilung| 18 | | Fähigkeitenkennwerte cₙ und cₘₖ | 3, 9 | - der Chiquadratverteilung | 18 | | Fähigkeitenzerwerte | 18, 28| R | | | Fertigungslage | 3, 28 | Rayleigh-Verteilung | 7 | | Fertigungsressourcen | 3, 6 | radiale Abweichung | 24 | | Fertigungsreihenfolge | 24 | Rohlgleichung | 24 | | Fertigungsgrad | 18 | Rundung von Fähigkeitswerten | 20 | | G | | Run-Test | 20 | | H | | Hampel-Test | 20 | | Häufigkeitsverteilung | 10, 17| Höchstmaß G₀ | 3, 9 | Image Analysis: ### 1. **Localization and Attribution:** There is only one image in the provided visual content. ### 4. **Text Analysis:** - **Detected Text:** **Title/Menu Section:** - Page number: "Seite 34" - Standard reference: "VW 101 30: 2005-02" - Section: "8 Stichwortverzeichnis" which translates to "8 Keyword Index". **Column Headers:** - "Stichwort" (Keyword) - "Seite" (Page) **Column Content:** - **Left Column:** - Keywords and page numbers listed alphabetically under the header "Stichwort" (Keywords) starting with letters A to H. - **Middle Column:** - Keywords and page numbers listed alphabetically under the header "Stichwort" (Keywords) starting with letters I to N. - **Right Column:** - Keywords and page numbers listed alphabetically under the header "Stichwort" (Keywords) starting with letters N to Z. - **Significance:** - This image appears to be a section of a technical or academic document, providing an index of keywords along with their respective page numbers. ### 13. **Graph Numbers (Tabular Data):** - **Left Column (A to H):** | Stichwort | Seite(s) | |--------------------------------|-------------| | absolute Häufigkeit α | 10, 17 | | absolute Summenhäufigkeit A | 17 | | α-Risiko | 20 | | Alternativhypothese | 20 | | angepasste Fähigkeitsgrenzwerte | 19, 28 | | Ausreißer | 20, 26 | | Aussagewahrscheinlichkeit γ | 20, 26 | | Bedingungen zur MFU | 24 | | β-Risiko | 20 | | Betragsverteilung 1. Art | 5, 11 | | Betragsverteilung 2. Art | 7, 13 | | betriebswarme Maschine | 24 | | Capability | 3 | | Chiquadrat-Verteilung | 18 | | Datenauswertung | 25 N | | Dichtenfunktion f(x) | 4 | | Dokumentation | 27 | | eingeschränkte MFU | 25 P | | effektiver Stichprobenumfang ne | 10, 24 | | Epps-Pulley-Test | 20, 26 | | Ergebnisbeurteilung | 28 | | Erwartungswert der v-Verteilung d_n | 17 | | Exzentrizität z | 7 | | Fähigkeitsbestimmung | 24 | | Fähigkeitskennwerte c_n und c_sink | 3, 9 | | Fähigkeitskennwerte | 18, 28 | | Fertigungslage | 3, 28 | | Fertigungsausrichtung | 3, 8 | | Fertigungsreihenfolge | 24 | | Fertigrad | 18 | - **Middle Column (I to N):** #################### File: VW%2010130_DE%281%29.pdf Page: 34 Context: - **Middle Column (I to N):** | Stichwort | Seite(s) | |------------------------------------|----------| | Irrtumswahrscheinlichkeit α | 20 | | Klassenbreite Δx | 20 | | klassierte Messwerte | 20 | | Korrekturfaktor k | 17 | | Lage | 3 | | Maschinenoptimierung | 29 | | Maschinenstörungen | 24 | | Medianwert | 16 | | Merkmalsart | 4, 25 | | Merkmalswert | 3 | | Messmethode | 24 | | Mindestmaß Gu | 3, 9 | | Mischverteilung | 26, 32 | | Mittelwert μ | 4, 10 | | Normalverteilung | 4, 10 | | Nullhypothese | 20 | | Nullpunktsverschiebung | 6 | | Parameter einer Verteilung | 3 | | Prüfgröße | 20 | | Prüfwert | 20 | | Prüfmitteleinwendung | 24 | | Quantil | 9 | | - der standardisierten Normalverteilung | 18 | | - der Chiquadratverteilung | 18 | - **Right Column (N to Z):** | Stichwort | Seite(s) | |--------------------------------|-----------| | Rayleigh-Verteilung | 7 | | radiale Abweichung r | 24 | | Rohteilcharge | 24 | | Rundung von Fähigkeitswerten | 18 | | Run-Test | 20 | | Streuparameter γ | 6 | | Streuung U | 41 | | technische Kenngrößen | 121 | | Teststatistik | 8 | | Trennschärfe ß | 29 | | Varianz σ² | 15 | | - der Normalverteilung | 14 | | Varianzparameter | 10 | | Verfahrensfähigkeit | 17 | | Verteilungspareto und Paretoprinzip|13 | | Wahrscheinlichkeitsfunktion P(x) | 8 | | This visual content appears as the keyword index section of a technical document or manual. It is structured to allow readers to quickly locate topics of interest within the broader document using page numbers. This is a common feature in detailed technical manuals, quality control guides, or educational textbooks. #################### File: VW%2010130_DE%281%29.pdf Page: 35 Context: # Stichwortverzeichnis | Stichwort | Seite | |---------------------------------------------|-------| | S | | | Schätzung / Schätzwert | 8, 9 | | Schwellenwert | 20 | | Serienbedingungen | 24 | | signifikante Änderung / Abweichung | 17 | | Spannweite R | | | Standardabweichung σ | 4, 10 | | standardisierte Normalverteilung | 5 | | - U-Transformation | | | - Verteilungsfunktion Φ(μ) | | | - Wahrscheinlichkeitsdichtefunktion f(x) | | | statistische Tests | | | statistische Toleranzrechnung | | | statistischer Anteilsbereich | | | Stichprobenahme | 24 | | Stichprobenumfang | 24 | | Streuungsgrenzen | 3, 10 | | Swed-Eisenhard-Test | 20 | | T | | | Test | | | - auf Ausreißer | 20, 26 | | - auf festgelegtes Verteilungsmodell | 20, 26 | | - auf Änderung der Fertigungslage | 20, 26 | | Toleranzerweiterung | 29 | | Toleranzintervall | 3, 8 | | toleriertes Merkmal | 4 | | - einseitig nach oben | 9, 16 | | - einseitig nach unten | 9, 16 | | - zweiseitig | 9, 16 | | Trendverlauf | 26 | | V | | | Varianz σ² | 4 | | Verteilung | 4 | | Verteilungsfreie Schätzung | 16, 27 | | Verteilungsfunktion F(x) | | | Verteilungsmodell | 4 | | Vertrauensbereichsgrenze | 18 | | Verbesserungsgüte | | | W | | | Wahrscheinlichkeit p | 5 | | Wahrscheinlichkeitsdichtefunktion f | | | Wahrscheinlichkeitnetz | 27 | | Publizitätverteilung | 28 | | Werkzeugwechsel / -verstellung | 24 | | Z | | | Zufallseinflüsse | 3 | Image Analysis: ## Comprehensive Examination Report: ### 1. Localization and Attribution - **Image 1:** This is the single image provided for analysis. It spans the entire page. ### 2. Object Detection and Classification - **Detected Objects:** - The image contains text, which appears to be an index or a list. - Objects: Columns of text. ### 3. Scene and Activity Analysis - **Scene Description:** - The scene consists of a neatly organized document page featuring an index or table of contents. - **Activities:** - No human activity is depicted. The action here is the informational purpose of the index. ### 4. Text Analysis - **Text Extraction:** - The page contains several keywords and their corresponding page numbers. - Column Headers: "Stichwort" (Keyword), "Seite" (Page). - Keywords: Various terms listed alphabetically with their page numbers. - Keywords span letters S to Z, with different associated numerical entries. - **Content Significance:** - The text appears to be from an index of a document or book, helping users find specific topics or terms. It's part of a larger document identified by "VW 101 30: 2005-02" on page 35. ### 7. Anomaly Detection - **Possible Anomalies:** - None detected. The index appears standard and formatted correctly. ### 8. Color Analysis - **Color Composition:** - Dominant Color: Black text on a white background. - The lack of other colors ensures clear readability and high contrast, aiding user navigation. ### 9. Perspective and Composition - **Perspective:** - The image is taken from a direct, head-on perspective typical for a document scan. - **Composition:** - The text is organized in two main columns with keywords on the left and corresponding page numbers on the right. The format is clean and structured, allowing easy navigation. ### 13. Graph Numbers - **Data Points:** - Keywords and page numbers are listed as follows: - **S:** - Schätzung: 8, 9 - Schätzwert: 8, 9 - Schwellenwert: 20 - Serienbedingungen: 24 - signifikante Änderung / Abweichung: 16 - Spannweite R: 17 - Standardabweichung: 4, 10 - standardisierte Normalverteilung: 5 - U-Transformation: 20 - Verteilungsfunktion: 16, 27 - Wahrscheinlichkeit: 4, 5 - statistische Toleranzrechnung: 29 - Werkzeugwechsel - verstellung: 24 - Zufalls einflüsse: 3 ### Additional Aspects - **Process Flows and Descriptions:** - Not applicable. This index page does not depict specific process flows or detailed process descriptions. - **Trend and Interpretation:** - Trends are not applicable because the image is an index page, not presenting trends or data variations. ### Summary - The image consists of page 35 from a larger document, labeled "VW 101 30: 2005-02." - It provides an alphabetical index of terms starting from "S" to "Z" and their associated page numbers. - The clean layout is functional, enhancing the ease with which users can locate topics within the document. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 1 Context: # Solutions for Powertrain **Volkswagen Group Components Global** **Differenzbeschreibung** --- **Ausgabe**: 01/2024 **Link**: [siemens.com/TRANSLINE](https://siemens.com/TRANSLINE) --- ## Technische Unterlage ### Overview This document provides comprehensive details on solutions for powertrains offered by Siemens for Volkswagen Group Components. It includes technological advancements, integration options, and support services available. ### Key Features - Advanced powertrain solutions - Tailored integration with Volkswagen components - Comprehensive support and consultancy services ### Specifications | Component | Description | |------------------|-----------------------------------------| | Electric Drive | High efficiency and performance | | Battery Management| Optimized charging and discharging | | Control Systems | Integrated for optimal performance | ### Benefits 1. **Increased Efficiency** - Reduced energy consumption 2. **Enhanced Performance** - Improved power delivery 3. **Sustainability** - Environmentally friendly solutions ### Conclusion The collaboration between Siemens and Volkswagen Group Components ensures leading-edge powertrain solutions that meet current and future mobility demands. --- For further details, please contact us through the provided link. Image Analysis: ### Analysis of Attached Visual Content: #### 1. Localization and Attribution: - **Image 1** is the only image on the page. #### 2. Object Detection and Classification: - **Objects Identified:** - **Car Outline:** A wireframe model of a car, which is a schematic representation showing the powertrain components. - **Powertrain Components:** - **Electric Motor and Transmission:** Visible components within the schematic of the car. - **Battery Pack:** Indicated below the car's chassis. - **Category:** Automotive engineering schematics. #### 3. Scene and Activity Analysis: - **Scene Description:** The image presents a technical illustration of a car's powertrain system, focusing on electric vehicle components. - **Activities:** No activities involving human actors are depicted. The image serves a technical and explanatory purpose to showcase the powertrain solution. #### 4. Text Analysis: - **Text Detected:** - "SIEMENS" - “TECHNISCHE UNTERLAGE” - “Solutions for Powertrain” - “Volkswagen Group Components Global” - “Differenzbeschreibung” - “Ausgabe 01/2024” - “siemens.com/TRANSLINE” - **Text Content Analysis:** - **"SIEMENS"** indicates the company responsible for the content. - **"TECHNISCHE UNTERLAGE"** translates to "Technical Documentation." - **"Solutions for Powertrain"** indicates the focus on powertrain technology solutions. - **"Volkswagen Group Components Global”** suggests collaboration or targeting of Volkswagen Group’s components. - **“Differenzbeschreibung”** translates to “Description of Differences,” likely detailing differences in powertrain components or solutions. - **“Ausgabe 01/2024”** indicates the issue date (January 2024). - **“siemens.com/TRANSLINE”** provides a URL for more information. #### 5. Diagram and Chart Analysis: - No charts or diagrams requiring analysis apart from the powertrain schematic within the car outline. #### 6. Product Analysis: - **Products Depicted:** - **Powertrain System:** Includes electric motor, battery pack, and transmission components. - **Main Features:** Highlighted with a neon-effect wireframe to emphasize the components' placement within the vehicle. #### 7. Anomaly Detection: - No anomalies or unusual elements detected in the image. #### 8. Color Analysis: - **Color Composition:** Dominant colors are blue and cyan used in the car's wireframe model and powertrain components. The background is a gradient of dark blue to black, enhancing the focus on the neon schematic. - **Impact:** The use of bright, neon colors against a dark background creates a high-contrast, futuristic, and technical aesthetic. #### 9. Perspective and Composition: - **Perspective:** The image is taken from an overhead/side angle, offering a clear view of the entire car and the embedded components. - **Composition:** Centralized composition of the car ensures focus on the powertrain system, with supporting text aligned to maintain visual balance. #### 10. Contextual Significance: - **Overall Document Context:** Likely part of a technical manual or brochure for automotive engineering solutions by Siemens for Volkswagen Group. - **Contribution to Overall Message:** Emphasizes Siemens' advanced technical solutions for automotive powertrain components, particularly for electric vehicles. #### 13. Ablaufprozesse (Process Flows): - The image implies a flow of process in powertrain integration within an electric vehicle, hinting at Siemens' involvement at various stages of component production and implementation. #### 14. Prozessbeschreibungen (Process Descriptions): - While detailed descriptions are not provided in the image, the title "Differenzbeschreibung" suggests the document contains detailed descriptions of differences or specific features in powertrain solutions. ### Summary: The single image analyzed presents a detailed schematic of a car's powertrain, specifically designed for electric vehicles, produced by Siemens in collaboration with Volkswagen Group Components Global. The technical illustration, along with the accompanying text, indicates this is a part of a technical document aimed at showcasing Siemens' advanced solutions for automotive powertrain systems, highlighted by futuristic design and clear, informative text. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 2 Context: # Projektspezifische Dokumentation ## Aufzeichnungsschlüssel Die nachfolgend aufgeführten Ausgaben sind bis zur vorliegenden Ausgabe erschienen. In der Spalte „Bemerkung“ ist durch Buchstaben gekennzeichnet, welchen Status die bisher erschienenen Ausgaben besitzen. ### Kennzeichnung des Status in der Spalte „Bemerkung“: - A .... Neue Dokumentation. - B .... Unveränderter Nachdruck mit neuer Ausgabe-Nummer. - C .... Überarbeitete Version mit neuem Ausgabenstand. | Ausgabe | Bemerkung | |----------|-----------| | 06/2011 | A | | 03/2012 | C | | 01/2013 | C | | 05/2013 | C | | 01/2015 | C | | 01/2018 | C | | 07/2018 | C | | 01/2020 | C | | 01/2021 | C | | 01/2022 | C | | 01/2023 | C | | 01/2024 | C | #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 3 Context: # Weitere Informationen Weitere Informationen finden Sie im Internet unter: [Siemens](http://www.siemens.com/information). Die Erstellung dieser Unterlage erfolgte mit Microsoft Word für Microsoft 365 MSO. ## Wichtige Hinweise Weder das Verfügbarmachen dieser Unterlage, Verwendung und Mitteilung ihres Inhalts ist gestattet, soweit nicht ausdrücklich zugestanden. Darüber hinausgehende Verpflichtungen zu Schadenersatz, Alle Rechte vorbehalten, insbesondere für den Fall der Patentierung oder GM-Eintragung. © Siemens AG 2024. All Rights Reserved. **Technische Änderungen vorbehalten.** Printed in the Federal Republic of Germany. Siemens Aktiengesellschaft. Es können weitere, in dieser Dokumentation nicht beschriebenen Funktionen in der Steuerung auffinden sein. Es besteht jedoch kein Anspruch auf diese Funktionen bei Neufertigung bzw. im Serieneinsatz. Wir haben den Inhalt der Druckschrift auf Übereinstimmung mit der beschriebenen Hard- und Software geprüft. Dennoch können Abweichungen nicht ausgeschlossen werden. Die Angaben in dieser Druckschrift werden regelmäßig überprüft, und notwendige Korrekturen sind in den nachfolgenden Auflagen enthalten. Für Verbesserungsvorschläge sind wir dankbar. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 4 Context: # Für Notizen **Notizen:** Hier können Sie alle wichtigen Informationen festhalten. ## Tabellen | Kategorie | Beschreibung | |-----------------|---------------------------| | Beispiel 1 | Beschreibung für Beispiel 1 | | Beispiel 2 | Beschreibung für Beispiel 2 | | Beispiel 3 | Beschreibung für Beispiel 3 | ## Listen ### Unordered List - Punkt 1 - Punkt 2 - Punkt 3 ### Ordered List 1. Erster Punkt 2. Zweiter Punkt 3. Dritter Punkt ## Links [Hier klicken für mehr Informationen](https://www.beispiel.com) ## Zitate > "Das ist ein Beispiel für ein Zitat." - Autor Für weitere Notizen können Sie die folgenden Bereiche nutzen. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 5 Context: # Inhalt Inhalt 0.5 ## 1 Allgemeines 1-1 ## 2 Ansprechpartner 2-1 ### 2.1 Zentrale Ansprechpartnerin Volkswagen Group Components 2-1 ### 2.2 Weitere Ansprechpartner 2-1 ### 2.3 Hotline und Customer Support 2-1 ### 2.4 Siemens-Volkswagen Powertrain Extranet 2-2 ## 3 Projekthandbuch 3-1 ### 3.1 SINUMERIK Softwareversionen und VW Startup Sets 3-1 #### 3.1.1 SINUMERIK ONE 3-1 #### 3.1.2 SINUMERIK 840D sl 3-2 ### 3.2 Lizenzierung 3-2 ### 3.3 S7-1500 Runtimeeinzenzen 3-3 ### 3.4 Registrierungen der Siemens Komponenten 3-4 ### 3.5 Sprachen der Bedienoberflächen 3-4 ### 3.6 Dokumentation 3-5 #### 3.6.1 Maschinen auf Basis SINUMERIK ONE (TIA Portal Engineering) 3-5 #### 3.6.2 Maschinen auf Basis SINUMERIK 840D sl (Classic Engineering) 3-6 #### 3.6.3 Maschinen auf Basis SIMATIC S7-1500 (TIA Portal Engineering) 3-6 ### 3.7 Vernetzung 3-7 ## 3.8 Berechtigungsstufenkonzept 3-8 ### 3.8.1 Vorbemerkungen 3-8 ### 3.8.2 Berechtigungsstufen 3-9 ### 3.8.3 Maschinenenden bei SINUMERIK-basierten Maschinen 3-9 ## 3.9 Uhrzeitsynchronisation 3-10 ### 3.9.4 Maschinen auf Basis SINUMERIK ONE oder SINUMERIK 840D sl 3-10 #### 3.9.4.1 Maschinen mit SINUMERIK Operate auf IPC427... 3-11 #### 3.9.4.2 Maschinen mit SINUMERIK Operate auf NCU... 3-11 #### 3.9.5 Maschinen auf Basis SIMATIC S7-1500 3-11 #### 3.9.5.1 HMI Lite... 3-11 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 6 Context: # Inhalt 01/2023 ## 3.10 Festlegungen zu SINAMICS S120 ............................................................... 3-14 ## 3.11 Roboteranbindung ..................................................................................... 3-15 ## 3.12 Energieeffizienz .......................................................................................... 3-15 ## 4 Überblick .......................................................................................................... 4-1 ## 5 Betriebsmittel-Freigabeseite ............................................................................ 5-1 ## 6 Applikationsbeispiele ....................................................................................... 6-1 ### 6.1 Mechanische Fertigung (SINUMERIK ONE) .................................................. 6-1 #### 6.1.1 Flexible Bearbeitungslinie ...................................................................... 6-2 #### 6.1.2 Maschine oder Lader/Portal auf CNC-Basis (ohne IPC) ........................ 6-3 #### 6.1.3 Maschine oder Lader/Portal auf CNC-Basis (mit IPC) ......................... 6-4 #### 6.1.4 Maschine oder Lader/Portal auf PLC-Basis ........................................... 6-5 ### 6.2 Mechanische Fertigung (SINUMERIK 840D sl) ............................................. 6-6 #### 6.2.1 Flexible Bearbeitungslinie ...................................................................... 6-6 #### 6.2.2 Maschine oder Lader/Portal auf CNC-Basis (ohne IPC) ....................... 6-7 #### 6.2.3 Maschine oder Lader/Portal auf CNC-Basis (mit IPC) ......................... 6-8 #### 6.2.4 Maschine oder Lader/Portal auf PLC-Basis .......................................... 6-9 ### 6.3 Montage ....................................................................................................... 6-11 #### 6.3.1 Montagelinie .......................................................................................... 6-11 #### 6.3.2 Zentralsteuerung .................................................................................. 6-12 #### 6.3.3 Automatisierungsstation ....................................................................... 6-13 #### 6.3.4 Handarbeitsplatz ................................................................................... 6-14 ## 7 Software Guide ................................................................................................ 7-1 ### 7.1 Maschinen auf Basis SINUMERIK ONE (TIA Portal Engineering) ............ 7-1 #### 7.1.1 Software Guide SINUMERIK ONE .......................................................... 7-1 #### 7.1.2 Programmierregeln SINUMERIK ONE .................................................. 7-2 #### 7.1.3 Projektierung von Baugruppenamen und PROFInet-Gerätenamen ..... 7-5 #### 7.1.4 Aufbau von HMI-PRO-Meldungen .......................................................... 7-6 ### 7.2 Maschinen auf Basis 840D sl (Classic Engineering) ............................... 7-7 #### 7.2.1 Software Guide 840D sl ......................................................................... 7-7 #### 7.2.2 Programmierregeln 840D sl ................................................................... 7-8 #### 7.2.3 Aufbau von HMI-PRO-Meldungen .......................................................... 7-8 ### 7.3 Maschinen auf Basis S7-1500 (TIA Portal Engineering) .......................... 7-9 #### 7.3.1 Programmierregeln S7-1500 .................................................................. 7-9 #### 7.3.2 Software Guide S7-1500 ....................................................................... 7-12 #### 7.3.3 GRAPH Schnittstelle S7-1500 ................................................................ 7-12 #### 7.3.4 ProDiag Diagnosesystem S7-1500 ........................................................ 7-14 #### 7.3.5 Safety-Vorgaben S7-1500 ....................................................................... 7-15 #### 7.3.6 Projektierung von Baugruppenamen und PROFInet-Gerätenamen ...... 7-19 ## 8 Visualisierung Bedienung Diagnose ............................................................... 8-1 ### 8.1 Bedienung Allgemein .................................................................................... 8-1 #### 8.1.1 Bedienfeld-Software ............................................................................... 8-1 #### 8.1.2 Bedienendgerät ...................................................................................... 8-3 ### 8.2 Bedienung SINUMERIK ONE ..................................................................... 8-4 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 7 Context: # Inhalt ## 8.1 Maschinensteuertafeln 8.1.1 Maschinensteuertafel MCP 190 ................................. 8-4 8.1.2 Maschinensteuertafel MCP 190 (VW Wolfsburg) .... 8-7 8.1.3 Push Button Panel MPP 464 .................................... 8-10 8.1.4 Erweiterungsblende .................................................... 8-13 ## 8.3 Bedienung SINUMERIK 840D 8.3.1 Maschinensteuertafel MCP 483 ................................. 8-15 8.3.2 Maschinensteuertafel MCP 483 (VW Wolfsburg) .... 8-18 8.3.3 Push Button Panel MPP 483 Volkswagen-Varianten .. 8-21 8.3.4 Erweiterungsblende .................................................... 8-25 ## 8.4 Belegung von Bedienplätzen 8.4.1 Bedienplätze ohne Maschinensteuertafel oder Push Button Panel .......................................... 8-26 8.4.2 Bedienplätze mit Maschinensteuertafel oder Push Button Panel .......................................... 8-27 8.4.3 Belegung von Bedienplätzen (VW Wolfsburg) .......... 8-28 - 8.4.3.1 Bedienplätze ohne Maschinensteuertafeln ............ 8-28 - 8.4.3.2 Bedienplätze mit Maschinensteuertafeln ............ 8-28 8.4.4 Belegung von Bedienplätzen (VW Kassel) ................. 8-29 ## 8.5 Visualisierung HMI Pro (SINUMERIK Panels) ............ 8-30 ## 8.6 Visualisierung HMI Lite (SIMATIC Panels) ................. 8-30 ## 9 Datensicherung ..................................................................... 9-1 ## 10 SINUMERIK 840D SI Safety Integrated 10.1 Hardwareaufbau Safety Integrated Stufe II (PROFIsafe) ............ 10-1 10.2 Kennzeichnung von Maschinen mit Safety Integrated ............... 10-5 10.3 Allgemeine Vorgaben für die Verwendung ........................... 10-5 10.4 Vorgaben für die Safety Integrated Abnahme ........................ 10-6 10.5 Abgleichmatrix ..................................................................... 10-7 10.6 Sichere programmierbare Logik ........................................ 10-7 10.7 Benutzerdefinierte Fehlermeldungen .................................. 10-8 ## 11 Parametrierung Anlagennetz ............................................. 11-1 ## 12 Betriebsdaten­erfassung 12.1 TRANSLINE Collect .......................................................... 12-1 12.1.1 Allgemeines .................................................................. 12-1 12.1.2 Lizenzen ..................................................................... 12-3 12.1.3 HMI PRO Bedienfeldschnittstelle ................................. 12-3 12.1.4 PLC Schnittstelle ......................................................... 12-4 12.1.5 Adapter .................................................................... 12-4 12.1.6 Server ....................................................................... 12-4 12.2 OPC UA Informationsmodell .......................................... 12-4 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 8 Context: # Inhaltsverzeichnis ## A Anhang - **Änderungsindex**......................................................................................... A-1 - A.1.1 Änderungen von Ausgabe 06/2011 auf Ausgabe 03/2012................................. A-1 - A.1.2 Änderungen von Ausgabe 03/2012 auf Ausgabe 01/2013................................. A-1 - A.1.3 Änderungen von Ausgabe 01/2013 auf Ausgabe 05/2013................................. A-1 - A.1.4 Änderungen von Ausgabe 05/2013 auf Ausgabe 01/2015................................. A-1 - A.1.5 Änderungen von Ausgabe 01/2015 auf Ausgabe 01/2018................................. A-1 - A.1.6 Änderungen von Ausgabe 01/2018 auf Ausgabe 07/2018................................. A-2 - A.1.7 Änderungen von Ausgabe 07/2018 auf Ausgabe 01/2020................................. A-2 - A.1.8 Änderungen von Ausgabe 01/2020 auf Ausgabe 01/2021................................. A-3 - A.1.9 Änderungen von Ausgabe 01/2021 auf Ausgabe 01/2022................................. A-3 - A.1.10 Änderungen von Ausgabe 01/2022 auf Ausgabe 01/2023............................... A-4 --- Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 9 Context: # 1 Allgemeines ## Einleitung Siemens stellt mit diesem Handbuch ein abgerundetes Konzept, ausgerichtet auf die Automatisierung der mechanischen Fertigung und Montage von Motoren, Achsen und Getrieben in der Automobilindustrie, dar. Grundlage hierfür sind die bewährten Produktfamilien SIMATIC, SINUMERIK, SINAMICS und SIMOTICS. Das Handbuch ist verpflichtend für alle involvierten OEMs während der Angebots- als auch Implementierungsphase. Applikationsbeispiele und eine Komponenten-Liste unterstützen die OEMs bei der Lieferung einer einheitlichen, standardisierten Lösung. Sie stellen die optimale Installation und Betrieb des Siemens Equipments sicher. In diesem Sinne dient das Handbuch auch als Rahmen für das Direktgeschäft zwischen Siemens und den OEMs bezüglich des Siemens Equipments im Projekt. Darauf aufsetzend entwickeln unsere Mitarbeiter zugeschnitten auf den jeweiligen Fertigungsbereich und auf die spezifischen Projektanforderungen die gewünschten Automatisierungslösungen einschließlich Kommunikation (PROFINET), Safety Integrated, Software, Engineering, Schulung, Ersatzteile und Service. Soweit der Endkunde im Projekt technische After-Sales Unterstützung zum Betrieb des Siemens Equipments benötigt, ist Siemens bereit marktgerechte Unterstützung in Form von Training, Ersatzteilen und Service zu leisten. Die Details zur Unterstützung während der Projektphase, normalerweise in der zweiten Inbetriebnahme und Anlaufphase, werden in der Projektimplementierungsphase zwischen Siemens und dem Endkunden definiert. Um eine schnelle Erbringung der Leistungen zu gewährleisten, wird die Unterstützung direkt von Siemens an den Endkunden erbracht. Ein Projektteam unterstützt Sie bei der Abwicklung sowie bei der technischen Ausarbeitung Ihrer Projekte. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 10 Context: # 1 Allgemeines 01/2024 ## Grundlage > **Wichtig** > Grundsätzlich gilt die TRANSLINE Standardhandbuchsammlung, Ausgabe 2024. > Sie finden diese Standardhandbuchsammlung im Solutions for Powertrain Extranet unter: > - **Startseite**: [https://www.siemens.com/sp-extranet](https://www.siemens.com/sp-extranet) > - **Pfad**: Transline Standard → Standardhandbücher → Ausgabe 2024 Abweichungen und Ergänzungen sind in dem vorliegenden volkswagenspezifischen Dokument beschrieben. ## Marken In diesem Dokument wird der Begriff „Volkswagen“ übergreifend für die einzelnen Konzernmarken des Volkswagen-Konzerns verwendet (z. B. VW, Audi, Seat, Skoda). ## Volkswagen Group Components Konzernstandard Das folgende Bild zeigt einen Überblick über die Elemente des Volkswagen Group Components Konzernstandards: ![Volkswagen Group Components Konzernstandard](path/to/image) ## Gültigkeit Die in dieser Differenzbeschreibung enthaltenen Abweichungen und Ergänzungen beschreiben alle volkswagenspezifischen Festlegungen zu der oben genannten zugrunde liegenden TRANSLINE Standardhandbuchsammlung. --- *Solutions for Powertrain / TRANSLINE* *© Siemens AG 2023 Alle Rechte vorbehalten* *Differenzbeschreibung Volkswagen Group Components Global* Image Analysis: ### Analysis of Attached Visual Content #### Localization and Attribution - The image is the sole visual content on the page. - Designated as **Image 1**. #### Text Analysis - **Detected Text & Content:** - **Main Title:** "1 Allgemeines 01/2024" - **Section Header:** "Grundlage" - **Content:** - "Wichtig" (Important) - "Grundsätzlich gilt die TRANSLINE Standardhandbuchsammlung, Ausgabe 2024. [...] - Hier ist das Dokument in dem volkswagen-spezifischen Dokument beschrieben." - **Section Header:** "Konzernmarken" - **Content:** - "In diesem Dokument wird der Begriff „Volkswagen“ übergreifend für die einzelnen Konzernmarken des Volkswagen-Konzerns verwendet (z.B. VW, Audi, Seat, Skoda)." - **Section Header:** "Volkswagen Group Components Konzernstandard" - **Content:** - "Das folgende Bild zeigt einen Überblick über die Elemente des Volkswagen Group Components Konzernstandards: [...] - Weltweite Projektkoordination durch Siemens, Siemens-Volkswagen Powertrain Extranet als Informationsplattform." - **Section Header:** "Gültigkeit" - **Content:** - "Die in dieser Differenzbeschreibung enthaltenen Abweichungen und Ergänzungen beschreiben [...] unter der oben genannte zugrundleingenden TRANSLINE Standardhandbuchsammlung." #### Diagram and Chart Analysis - **Image 1: Diagram Overview** - **Title:** Volkswagen Group Components Konzernstandard - **Sections within the Diagram:** - **Freigabelisten:** TRANSLINE Niederspannungsschalttechnik - **HMI-Standards:** HMI PRO (VW Standard) (CNC-Maschinen), HMI Lite (VW Standard) (SPS-Maschinen) - **Projekthandbuch:** Volkswagen Group Components Global - **VW Master DVDs and Startup Sets:** Software Standard for CNC-Steuerte Komponenten - **Footer Note:** "Weltweite Projektkoordination durch Siemens, Siemens-Volkswagen Powertrain Extranet als Informationsplattform" #### Scene and Activity Analysis - **Scene Description:** - The scene presents a structured document page with multiple information sections, including a detailed diagram in the middle of the page. - **Main Activity:** - The text and diagram articulate the standards, guidelines, and organizational details regarding Volkswagen Group components and their coordination managed through Siemens platforms. #### Color Analysis - Dominant Colors: - Shades of white, gray, and blue - Impact on Perception: - Creates a professional and formal appearance, suitable for corporate documentation. #### Perspective and Composition - **Perspective:** - The page has a standard front-facing view, typical for reading documents. - **Composition:** - Information is hierarchically structured with headings, subheadings, and a centered diagram for visual effectiveness. ### Summary of Visual Content Analysis This page serves as an introduction section for a document concerning Volkswagen Group Components Konzernstandard with information about relevant standards and documentation managed primarily through Siemens. The diagram in the middle visually outlines the specific elements of the Konzern standard, simplifying complex standards into categorized sections. This layout aids in clear and structured communication of significant corporate guidelines. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 11 Context: # 01/2023 1 Allgemeines > **Wichtig** > Es ist für CNC-basierte Maschinen das System SINUMERIK ONE oder SINUMERIK 840D SL und für PLC-basierte Maschinen > das System SIEMENS S7-1500 gemäß Freigabeliste einzusetzen. > Als Antriebssysteme sind SIMANICS-Antriebe gemäß Freigabeliste einzusetzen. > Für die anlagenspezifische Auswahl der Steuerung und Software-Versionen ist zwingend eine Abstimmung mit der zuständigen Elektrofachabteilung notwendig. > > Bei Umbau oder Ergänzung der vorhandenen Fertigungs- oder Montageeinrichtungen ist zwingend eine Rücksprache mit der zuständigen Elektrofachabteilung notwendig. Das Ergebnis über die einzusetzenden Stände für Soft- und Hardware ist schriftlich festzuhalten. > > Die in diesem Dokument enthaltenen Abschnitte gelten nur, wenn die beschriebenen Komponenten in der für das jeweilige Projekt gültigen Betriebsmittel-Freigabeliste freigegeben sind. ## Aktualisierungen und ergänzende Informationen zum Projekthandbuch > **Wichtig** >Evtl. Aktualisierungen und ergänzende Informationen zum vorliegenden Projekthandbuch finden Sie im Siemens-Volkswagen >Powertrain Extranet (vergl. Kap. 2). © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global Solutions for Powertrain / TRANSLINE 1 - 3 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 12 Context: # 1 Allgemeines 01/2024 ## Für Notizen --- **Solutions for Powertrain / TRANSLINE** Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 13 Context: # 2 Ansprechpartner ## 2.1 Zentrale Ansprechpartnerin Volkswagen Group Components Hr. Markus Siebler Siemens Erlangen Tel. +49 (172) 898-8019 [markus.siebler@siemens.com](mailto:markus.siebler@siemens.com) ## 2.2 Weitere Ansprechpartner Weitere technische Ansprechpartner sowie die lokalen Siemens-Ansprechpartner für die jeweiligen Powertrain-Werke finden Sie im Siemens-Volkswagen Powertrain Extranet unter "Kontakte". ## 2.3 Hotline und Customer Support | Service | Kontakt | |------------------|----------------------------------------------| | SiePortal (Support) | [sieportal.siemens.com](https://sieportal.siemens.com/) | | TRANSLINE Support | transline_support.industry@siemens.com | | | Tel. +49 (711) 6521-3068 | #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 14 Context: ## 2.4 Siemens-Volkswagen Powertrain Extranet Im Siemens-Volkswagen Powertrain Extranet finden Sie Informationen zur Standardisierung in der Volkswagen Group Components Produktion. Neben den Siemens-seitigen Elementen des Volkswagen Group Components-Konzernstandards finden Sie hier auch Informationen zu einzelnen Projekten, sowie Dokumentationen und HMI-Musterprojekte. **Startseite:** [https://www.siemens.com/sfp-extranet/vw](https://www.siemens.com/sfp-extranet/vw) Das Siemens-Volkswagen Powertrain Extranet ist Passwort-geschützt. Um Zugriff zu erhalten, verwenden Sie bitte den folgenden Link: [https://www.siemens.com/sfp-extranet/register/vw](https://www.siemens.com/sfp-extranet/register/vw) #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 15 Context: # 3 Projekthandbuch ## 3.1 SINUMERIK Softwareversionen und VW Startup Sets **Hinweis** Bitte beachten Sie die Beschreibung der verfügbaren VW Startup Sets im Siemens-Volkswagen Powertrain Extranet unter: - **Startseite**: [siemens.com/sfp-extranet/vw](https://www.siemens.com/sfp-extranet/vw) - **Pfad**: Global → VW Master DVDs und Startup Sets Falls bereits aktuelle Versionen der VW Startup Sets, als die hier angegebenen verfügbar sind, ist zwingend mit der zuständigen Elektrofachabteilung Rücksprache zu halten. **Wichtig** Wenn ein PC-basiertes SINUMERIK HMI verwendet wird, ist der IPC427E gemäß Freigabeiblen einzusetzen. Bitte beachten Sie, dass je nach verwendeter Betriebsystemversion jeweils die passende Variante des IPC427E verwendet werden muss. ### 3.1.1 SINUMERIK ONE **Wichtig** Für die SINUMERIK ONE ist die Exportversion der SINUMERIK Systemssoftware Version 6.15 (oder neuer) einzusetzen. Als Software für das Bedienen & Beobachten für Maschinen auf Basis SINUMERIK ONE ist folgendes VW Startup Set zu verwenden: - **IPC47xE_W10_6.1_V1.0.1** auf Basis Windows 10 Enterprise 2019 LTSC #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 16 Context: # 3 Projekthandbuch 01/2024 ## 3.1.2 SINUMERIK 840D sl **Wichtig:** Für die SINUMERIK 840D sl ist die Exportversion der SINUMERIK Systemssoftware Version 4.95 (oder neuer) einzusetzen. Als Software für das Bedienen & Beobachten für Maschinen auf Basis SINUMERIK 840D sl sind je nach Software-Version die folgenden VW Startup Sets zu verwenden: - IPC47xE_W10_4.9_V1.0.1 - auf Basis Windows 10 Enterprise 2019 LTSC **Wichtig:** Wenn Sie dieses Startup Set mit einem IPC427E mit einer Lizenz für Windows 10 Enterprise 2016 LTSB oder älter verwenden, benötigen Sie ein IPC Operating System Package, Artikelnummer 6ES7648-6WC21-1YA0. Weitere Informationen zu diesem Thema finden Sie in der folgenden Produkttmitteilung: [https://support.industry.siemens.com/cs/de/de/view/109780443](https://support.industry.siemens.com/cs/de/de/view/109780443) ## 3.2 Lizenzierung **Wichtig:** Ist die Software oder ein Teil der Software urheberrechtlich geschützt, müssen die Lizenzverträge mit dem Nachweis des übertragenen Nutzungsrechts und evtl. Copyright-Vermerken bei der Übergabe der Anlage vorhanden sein und mit übergeben werden. **Hinweis:** Beim Einsatz der Startup Sets müssen die jeweiligen Softwarelizenzen je Bedienfeld zusätzlich separat bestellt und mit übergeben werden. ### Lizenznachweis Das Certificate of License (CoL) bzw. das elektronische Certificate of License (eCoL) ist für den Lizenznehmer der Nachweis, dass die Nutzung der Software von Siemens lizenziert ist. Jede Nutzung ist ein CoL zuzuordnen, das sorgfältig aufzubewahren bzw. zu archivieren ist. --- *Solutions for Powertrain / TRANSILINE* © Siemens AG 2023 Alle Rechte vorbehalten *Differenzbeschreibung Volkswagen Group Components Global* 3-2 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 17 Context: # 3 Projekthandbuch Vom Maschinenlieferanten müssen die Lizenznachweise sämtlicher eingesetzter Softwareprodukte sowie eine Liste der Softwarelizenzen an die zuständige Elektrofachabteilung übergeben werden. Dabei sind die Lizenzen für sämtliche Bereiche wie z. B. Steuerung, Antrieb, HMI-Software etc. zu berücksichtigen. ## 3.2.3 S7-1500 Runtime-Lizenzen Für die S7-1500 sind für die Nutzung einiger Funktionalitäten Runtime-Lizenzen notwendig. ### ProDiag | Software | Lizenz | |-------------------------------------|-----------------------------| | SIMATIC ProDiag S7-1500, Single Runtime License Download enthält Lizenzzertifikat für 250 Überwachungen, als pdf zum Download, Klasse A; ablaufähig auf allen S7-1500 ab Firmware V2.0. ***** Warenempfänger E-Mail Adresse zur Auslieferung erforderlich | 6ES7823-0AE00-1AA0 | | SIMATIC ProDiag S7-1500, Single Runtime License Download enthält Lizenzzertifikat für Freischaltungen aller projektierten Überwachungen in einer CPU, als pdf zum Download, Klasse A; ablaufähig auf allen S7-1500 ab Firmware V2.0. ***** Warenempfänger E-Mail Adresse zur Auslieferung erforderlich | 6ES7823-0AE00-1DA0 | ### OPC UA Server | Software | Lizenz | |-------------------------------------|-----------------------------| | SIMATIC OPC UA S7-1500 Small, Single Runtime License Download enthält Lizenzzertifikat für OPC UA Server und OPC UA Client Klasse A; ablaufähig auf allen ET 200SP CPU, S7-1500 bis CPU-1513, CPU 1505SP, CPU 1504D, inkl. F und T Derivaten ab Firmware V2.0. ***** Warenempfänger E-Mail Adresse zur Auslieferung erforderlich | 6ES7823-0BE00-1BA0 | #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 18 Context: ```markdown # 3 Projekthandbuch ## 01/2024 | Software | Lizenz | |-----------------------------------------------------------------------------------------|---------------------| | SIMATIC OPC UA S7-1500 Medium, Single Runtime License Download enthält Lizenzzertifikat für OPC UA Server und OPC UA Client Klasse A, Ablaffähig auf allen ET 200SP CPU, S7-1500 BIS CPU-1516, CPU 1507S, inklusive F und D Derivaten ab Firmware V2.0, OPC UA Server Method Call, Custom Address Space ab Firmware 2.5 ****** Warenempfänger E-Mail Adresse zur Auslieferung erforderlich | 6ES7823-0BE00-1CA0 | | SIMATIC OPC UA S7-1500 Large, Single Runtime License Download enthält Lizenzzertifikat für OPC UA Server und OPC UA Client Klasse A, Ablaffähig auf allen ET 200SP CPU, allen S7-1500 CPU, CPU 1508S, CPU 1507D, inklusive F und D Derivaten ab Firmware V2.0, OPC UA Server Method Call, Custom Address Space ab Firmware 2.5 ****** Warenempfänger E-Mail Adresse zur Auslieferung erforderlich | 6ES7823-0BE00-1DA0 | ## 3.3 Registrierung der Siemens Komponenten Für die Planung des weltweiten Service und Supports für Maschinen und Anlagen mit Siemens-Komponenten ist es zwingend erforderlich, dass der Maschinenhersteller seine Maschinen inklusive Stückliste in elektronischer Form bei Siemens unter folgendem Link registriert: [Siemens Registration](https://myregistration.siemens.com/startup) > **Wichtig** > Bei der Maschinenabnahme ist die erfolgte Registrierung durch die Übergabe eines Zertifikats nachzuweisen. Bei Rückfragen zur Registrierung ist Ihnen gerne Ihr lokaler Siemens-Ansprechpartner behilflich. ## 3.4 Sprachen der Bedienoberflächen Die Bedienoberfläche ist in folgenden Sprachen auszuführen: - Landessprache des jeweiligen Aufstellortes - plus Plansprache des Lastenhefts Eine englische Bedienoberfläche kann bei Bedarf zusätzlich mitgeteilt werden. ``` #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 19 Context: # 3 Projekthandbuch ## 3.5 Dokumentation Die Siemens-Dokumentation (Deutsch/Englisch) für die eingebauten Komponenten muss nicht vom Maschinenhersteller geliefert werden, sondern wird im Siemens Industry Online Support (SIOS) bereitgestellt. ## 3.6 Einzusetzende Softwareversionen für die Projektierung Für die Software-Projektierung sind auf dem Programmiergerät folgende Software-Versionen einzusetzen. ### 3.6.1 Maschinen auf Basis SINUMERIK ONE (TIA Portal Engineering) | Beschreibung | Version | Artikelnummer | Bemerkung | |-------------------------------|---------|----------------------|---------------------------------------------------------------------------| | SIMATIC STEP 7 Professional | V19 | 6ES7822-1AA23-0YA5 | Floating License auf DVD | | SIMATIC STEP 7 Safety Advanced | V19 | 6ES7833-1FA23-0YA5 | Floating License auf USB, zur Erstellung sicherheitsgerichteter Automatisierungsanwendungen mit SINUMERIK ONE nötig | | HMI PRO CS (Create MyHMI /pro) | gem. d. eingesetzten VW Startup Sets | - | Die Software ist lizenzfrei und ist auf dem jeweiligen VW Startup Set enthalten | ### 3.6.2 Maschinen auf Basis SINUMERIK 840D sl (Classic Engineering) | Beschreibung | Version | Artikelnummer | Bemerkung | |-------------------------------|---------|----------------------|---------------------------------------------------------------------------| | SIMATIC STEP 7 | V5.7 HF1 | 6ES7810-4CC12-0YA5 | Floating-License für 1 User, Software auf DVD, License Key auf USB-Stick | | S7-GRAPH | V5.7 HF1 | 6ES7811-0CC08-0YA5 | Floating-License für 1 User, Software auf CD, License Key auf USB-Stick | | HMI PRO CS (Create MyHMI /pro) | gem. d. eingesetzten VW Startup Sets | - | Die Software ist lizenzfrei und ist auf dem jeweiligen VW Startup Set enthalten | #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 20 Context: # 3.6.3 Maschinen auf Basis SIMATIC S7-1500 (TIA Portal Engineering) | Beschreibung | Version | Artikelnummer | Bemerkung | |--------------------------------------------|---------|------------------------|--------------------------------------------------------------------| | SIMATIC STEP 7 Professional | V19 | 6ES7822-1AA23-0YA5 | Floating License auf DVD | | SIMATIC STEP 7 Safety Advanced | V19 | 6ES7833-1FA23-0YA5 | Floating License auf USB, zur Erstellung sicherheitgesteuerter Automatisierungsanwendungen mit SIMATIC S7-1500 nötig | | SIMATIC WinCC Unified Engineering System Base Packages | V19 | 6AV2153-2FB02-3AA5 | Empfohlen für Unified Comfort Panel | | WinCC Unified PC (10k) ES V19 | V19 | 6AV2153-2GB02-3AA5 | Empfohlen für IPC und Sinumerik | | SIMATIC WinCC Unified Engineering System Base Packages | V19 | 6AV2101-0AA02-3AH5 | Projektierungssoftware, ohne Runtime Lizenzen | | SINAMICS Startdrive Advanced | V19 | 6SL3072-4KA02-0XA5 | Floating License auf DVD, Engineering- und Inbetriebnahmetool für SINAMICS Antriebe | ## Hinweis Nach Rücksprache mit der zuständigen Elektrofachabteilung kann für komplexe Anwendungen weiterhin das Inbetriebnahme-Tool STARTER verwendet werden. Sie finden die aktuelle STARTER Version im Siemens Industry Online Support unter: [Siemens Support](https://support.industry.siemens.com/cs/ww/de/view/26233208) #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 21 Context: # 3.7 Vernetzung ## Ethernet Die Ethernet-Adressenvergabe ist mit der zuständigen Elektrofachabteilung abzustimmen. ### Maschinen auf Basis SINUMERIK ONE oder 840D sl > **Wichtig** > Das Netzwerk für die Bedienkomponenten (Schnittstelle X120 der SINUMERIK NCU) und das Fabriknetz (Schnittstelle X130 der SINUMERIK NCU) sind physikalisch getrennte Netzwerke auszuführen. > > Die Vorgaben für die Ethernet-Adresse der Schnittstelle X130 (Fabriknetz) der SINUMERIK NCU sind vom Maschinenlieferanten mit der zuständigen Elektrofachabteilung / IT zu klären. > > Bei der SINUMERIK NCU sind die Firewall-Einstellungen für das Firmennetz (Schnittstelle X130) wie folgt zu setzen: > > - S7 Kommunikation zulassen (Port 102) > - VNC-Zugang deaktivieren (Port 5900) > - SSH deaktivieren (Port 22) ### Hinweis Bei Verwendung des IPC427E ist die Schnittstelle X1 für den Anschluss an das Fabriknetz zu reservieren. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 22 Context: # 3.8 Berechtigungsstufenkonzept **Wichtig:** Für VW Wolfsburg, Bereich Fahrwerk, VW Braunschweig und VW Kassel gilt ein eigenständiges EKS-Berechtigungsstufenkonzept. Bitte halten Sie dazu Rücksprache mit der zuständigen Elektrofachabteilung. ## 3.8.1 Vorbemerkungen **Hinweis:** Beim Einsatz des Electronic Key Systems (EKS) erfolgt die Anmeldung durch das Stecken eines Keys. In diesem Fall werden keine Passwörter verwendet und die Möglichkeit zur Eingabe von Passwörtern muss deaktiviert werden. Weitere Hinweise zum Anschluss des EKS-Lesers finden Sie in den jeweiligen Applikationsbeispielen in Kapitel 6. | Maschinen Typ | Beschreibung | |-------------------------------------|-------------------------------------------------------------------------------------------------------------------------| | SINUMERIK-basierte Maschinen mit HMI PRO | Es ist die Ethernet-Variante des EKS-Lesers zu verwenden. Die Integration des EKS-Lesers erfolgt automatisch durch die Nutzung der Softwareoption „SINUMERIK 840D SL Electronic Key System (EKS)“ (Artikelnr. 6FC5800-0AP53-0YB0). Es ist keine Programmierung notwendig. Weitere Hinweise finden Sie in der Online-Hilfe von HMI PRO. | | SIMATIC-basierte Maschinen mit SIMATIC Panels und HMI Lite oder Create MyHMI / Automotive (CMH) | Es ist die PROFINET-Variante des EKS-Lesers zu verwenden. In HMI Lite und CMH werden Standardbausteine zum Lesen des EKS Keys bereitgestellt. Die Schutzart muss in der SPS-Programmierung entsprechend berücksichtigt werden. Weitere Hinweise finden Sie im HMI Lite oder CMH Standardhandbuch nach der Installation auf dem lokalen Laufwerk oder in der TIA Hilfe Funktion. Das Schutzkonzept für den Einsatz von SIMATIC Panels ist mit der zuständigen Elektrofachabteilung abzustimmen. | #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 23 Context: # 3.8.2 Berechtigungstufen Neben den Standardeinstellungen gelten folgende Festlegungen: | Standard Siemens Berechtigungstufen | Berechtigung | Variante 1 Passwort bzw. BKS E7 (nur bei SINUMERIK-basierten Maschinen) | Variante 2 Euchner EKS | |--------------------------------------|----------------------------------|--------------------------------------------------------------------------|-------------------------------------| | Berechtigungsstufe 1 (Maschinenhersteller) | Hersteller, Service, Instanthalter | SUNRISE | Berechtigungsstufe 1 roter Key blauer Key (OEM) | | Berechtigungsstufe 2 (Inbetriebnehmer, Service) | Nicht verwendet | Nicht verwendet | Nicht verwendet | | Berechtigungsstufe 3 (Endanwender) | Nicht verwendet | Nicht verwendet | Nicht verwendet | | Berechtigungsstufe 4 (Programmierer, Einrichter) | Einrichter, Programmierer | Schlüsselschalter BKS E7 | Berechtigungsstufe 4 grüner Key | | Berechtigungsstufe 5 (qualifizierter Bediener) | Nicht verwendet | Nicht verwendet | Nicht verwendet | | Berechtigungsstufe 6 (Ausgebildeter Bediener) | Bediener | Nicht verwendet | Berechtigungsstufe 6 schwarzer Key | | Berechtigungsstufe 7 (angelernter Bediener) | Keine besondere Berechtigung | Kein Schlüssel | Kein Key | # 3.8.3 Maschinendaten bei SINUMERIK-basierten Maschinen Folgende Änderungen der allgemeinen Maschinendaten sind in den Volkswagen-Projekten erforderlich: | Maschinendatum | Bezeichnung | Schutzstufe | |----------------|--------------------------------------------------|-------------| | MD 11160 | Schutzstufe Ausführungsrecht / N_CST_DIR | 4 | | MD 11161 | Schutzstufe Ausführungsrecht / N_CUS_DIR | 4 | | MD 51044 | Schutzstufe SBL2 anzeigen | 7 | Image Analysis: ***Comprehensive Examination of Attached Visual Content:*** ### 1. Localization and Attribution - The visual content consists of two main sections. - **Section 1:** Table detailing "Berechtigungsstufen" - **Section 2:** Table detailing "Maschinendaten bei SINUMERIK-basierten Maschinen" ### 2. Object Detection and Classification - **Image 1:** - **Objects Detected:** 1. Table 2. Icons (Euchner EKS, Key, Lock) - **Image 2:** - **Objects Detected:** 1. Table 2. Text ### 3. Scene and Activity Analysis - **Image 1:** The scene includes a table categorizing various authorization levels (Berechtigungsstufen) in a structured manner. - **Image 2:** The scene includes a table specifying the required changes in general machine data for SINUMERIK-based machines in Volkswagen projects. ### 4. Text Analysis - **Image 1:** - **Header:** 3.8.2 Berechtigungsstufen (Authorization Levels) - **Content:** - Standard Siemens Authorization Levels - Different authorization levels with descriptions and variants - **Significance:** This section specifies authorization levels and their respective categories necessary for different roles and responsibilities. - **Image 2:** - **Header:** 3.8.3 Maschinendaten bei SINUMERIK-basierten Maschinen - **Content:** - Changes required in general machine data specific to Volkswagen projects - Detailed entries for machine data items and their respective security levels (Schutzstufe) - **Significance:** This section outlines necessary modifications to machine data to fit specific project requirements. ### 5. Diagram and Chart Analysis - There are no explicit diagrams or charts in the visual content. ### 6. Product Analysis - There are no specific products depicted in the visual content. ### 7. Anomaly Detection - **Image 1:** No anomalies detected. - **Image 2:** No anomalies detected. ### 8. Color Analysis - **Image 1:** - Dominant colors: Light grey background with black text and colored icons. - Impact: The light grey background and black text create a clear contrast, making the information easily readable. Colored icons help to differentiate between variants. - **Image 2:** - Dominant colors: Light grey background with black text. - Impact: The consistent color scheme maintains readability and emphasizes the textual content. ### 9. Perspective and Composition - **Perspective:** - Top-down view for both images. - **Composition:** - **Image 1:** - Structured table layout with distinct sections for authorization levels, variants, and their respective categories. - **Image 2:** - Well-organized table listing machine data changes and their security levels. ### 10. Contextual Significance - **Image 1:** - Provides essential information about authorization levels within the context of Siemens-based projects, likely part of a larger project handbook. - **Image 2:** - Details specific machine data adjustments necessary for SINUMERIK-based machines, indicating compliance and configuration requirements for Volkswagen projects. ### 12. Graph and Trend Analysis - There are no graphical data or trends explicitly visualized in the images. ### 13. Graph Numbers (Tables) - **Image 1:** - **Table Cells:** 1. Authorization Level 1: "Hersteller, Service, Instandhalter", "SUNRISE", "Berechtigungsstufe 1 roter Key blauer Key (OEM)" 2. Authorization Level 4: "Einrichter, Programmierer", "Schlüsselschalter BKS E7", "Berechtigungsstufe 4 grüner Key" 3. Authorization Level 6: "Bediener", "Nicht verwendet", "Berechtigungsstufe 6 schwarzer Key" 4. Authorization Level 7: "Keine besondere Berechtigung", "Kein Schlüssel", "Kein Key" - **Image 2:** - **Table Cells:** 1. MD 11160: "Schutzstufe Ausführungsrecht / _N_CST_DIR", "4" 2. MD 11161: "Schutzstufe Ausführungsrecht / _N_CUS_DIR", "4" 3. MD 51044: "Schutzstufe SBL2 anzeigen", "7" ### Additional Aspects - **Ablaufprozesse (Process Flows) and Prozessbeschreibungen (Process Descriptions):** Not explicitly depicted in the images. - **Typen Bezeichnung (Type Designations):** Indicated in the table categories, such as authorization levels and machine data names. - **Trend and Interpretation:** No discernible trends, as data is more categorical. - **Tables:** Both sections feature tables organizing important role-based authorizations and machine data. ### Conclusion The visual content comprises two key parts: authorization levels for Siemens-based systems and necessary machine data changes for SINUMERIK-based machines in Volkswagen projects, presented in clear tables with detailed descriptions. The information is highly relevant for project management and system configurations. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 24 Context: # 3 Projekthandbuch ## 01/2024 | Maschinen- datum | Bezeichnung | Schutz- Stufe | |-------------------|---------------------------------------------|----------------| | MD 51045 | Schutzstufe TEACH IN | 4 | | MD 51046 | Schutzstufe R-Parameter löschen | 4 | | MD 51047 | Schutzstufe Anwendervariable lesen | 7 | | MD 51048 | Schutzstufe Anwendervariable schreiben | 4 | | MD 51049 | Schutzstufe Programmbeeinflussung schreiben | 4 | | MD 51050 | Schutzstufe Teilprogramme schreiben | 4 | | MD 51051 | Schutzstufe R-Parameter schreiben | 4 | | MD 51052 | Schutzstufe Settingdaten schreiben | 4 | | MD 51060 | Schutzstufe einstellbar NV (G54-G599) schreiben | 1 | | MD 51200 | Schutzstufe WZW Geometriedaten schreiben | 6 | | MD 51201 | Schutzstufe WZW Verschieb Daten schreiben | 6 | | MD 51208 | Schutzstufe WZW Adapterdaten schreiben | 6 | | MD 51211 | Schutzstufe WZW Daten lesen | 7 | Es ist sicherzustellen, dass der Passwortschutz nach Abschluss der Bedienung nach 15 Min. automatisch zurückgesetzt wird. In HMI PRO ist für das Verfahren von NC-Achsen über Einrichtbild die Schutzstufe 6 einzuziehen. Der Maschinenlieferant hat sicherzustellen, dass der vereinbarte Zugriffs-schutz bei Verlassen der Anlage aktiv ist. Die Vereinbarungen sind schriftlich festzuhalten. ## 3.9 Uhrzeitsynchronisation **Wichtig:** Es gelten die Vorgaben der einzelnen Standorte. Deshalb ist für die Ausführung der Uhrzeitsynchronisation zwingend eine Rücksprache mit der zuständigen Elektroabteilung notwendig. ## 3.9.4 Maschinen auf Basis SINUMERIK ONE oder SINUMERIK 840D sl **Wichtig:** Die Synchronisation der Uhrzeit findet immer vom Bedienfeld zur NC/PLC statt! Image Analysis: ### Comprehensive Examination #### 1. Localization and Attribution - **Page Layout**: - **Top Section**: Header information and a table. - **Middle Section**: Paragraphs of text with highlighted instructions. - **Bottom Section**: Image with a graphical user interface followed by more text. #### 2. Object Detection and Classification - **Image 1 Information**: - **Table**: Contains machine data, descriptions, and protection levels. - **Controllers**: Blue GUI elements representing control buttons. #### 3. Scene and Activity Analysis - **Image 1 Scene**: - **Table**: Lists machine data and corresponding protection levels. - **Graphical Interface**: Shows a control panel layout for configuring NC-Axes. #### 4. Text Analysis - **Top Table**: - **Column Headers**: Machine Data, Description, Protection Level. - **Rows**: Lists various MD numbers with their protection levels and descriptions (e.g., MD 51045 - Schutzstufe TEACH IN - 4). - **Body Text**: - **Paragraph**: Explains the auto-reset feature for passwords after 15 minutes. - **Procedural Text**: Instructions for HMI PRO regarding NC-Axes and the protection level. - **Highlighted Text "Wichtig"**: - **Text Content**: Important notes about regulations for time synchronization and machine synchronization procedures. #### 5. Diagram and Chart Analysis - **Graphical Interface**: - **Content**: Controls related to machine configuration, labeled with instructions like 'Minus', 'X Achse', 'ENDW'. #### 6. Product Analysis - **Graphical User Interface**: - **Features**: Interactive buttons predominantly in blue. - **Labels**: Instructions for machine configuration. #### 7. Anomaly Detection - No specific anomalies are detected. #### 8. Color Analysis - **Dominant Colors**: Blue (buttons), black and white (text and background). - **Impact**: The colors help in distinguishing interactive elements from the textual instructions. #### 9. Perspective and Composition - **Perspective**: Straight-on, user interface perspective. - **Composition**: Structured, with clear demarcation between text blocks, table, and graphical interface. #### 12. Graph and Trend Analysis - **Trend**: Shows a consistent focus on security features across different MD numbers with varying protection levels. #### 13. Graph Numbers - **Table Data Points**: - **MD 51045**: Schutzstufe TEACH IN - 4 - **MD 51046**: Schutzstufe R-Parameter löschen - 4 - **MD 51047**: Schutzstufe Anwendervariable lesen - 7 - **MD 51048**: Schutzstufe Anwendervariable schreiben - 4 - **MD 51049**: Schutzstufe Programbeeinflussung schreiben - 4 - **MD 51050**: Schutzstufe Teilprogramme schreiben - 4 - **MD 51051**: Schutzstufe R-Parameter schreiben - 4 - **MD 51052**: Schutzstufe Settingdaten schreiben - 4 - **MD 51060**: Schutzstufe einstellbare NW schreiben - 1 - **MD 51200**: Schutzstufe WZV Geometriedaten schreiben - 6 - **MD 51201**: Schutzstufe WZV Verschleißdaten schreiben - 6 - **MD 51208**: Schutzstufe WZV Adapterdaten schreiben - 6 - **MD 51211**: Schutzstufe WZV Daten lesen - 7 #### 14. Ablaufprozesse (Process Flows) - **Detail**: Process for protecting traceability and configuration of NC-Axes in HMI PRO. #### 16. Typen Bezeichnung (Type Designations) - **Controlled Processes**: List of different types of protective measures (e.g., Anwendervariable lesen/schreiben). #### Contextual Significance - **Overall Document**: Likely part of procedural documentation for machine configuration, emphasizing security and regulatory compliance. ### Summary The attached visual content provides detailed instructions on machine data protection levels, includes procedural guidelines for synchronization and security, and features a graphical interface for configuring NC-Axes. Tables and highlighted sections underscore important instructions, clearly demarcating user actions required for machine maintenance and configuration. The use of blue in the interface aids in highlighting control features, ensuring clarity in usage instructions. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 25 Context: # 3 Projekthandbuch Beim Einsatz von HMI PRO geschieht dies automatisch im Hochlauf der Anlage, danach dann ein Mal pro Stunde. ## 3.9.4.1 Maschinen mit SINUMERIK Operate auf IPC427 Die Einstellung von Datum und Uhrzeit erfolgt unter: „IBN“ > „HMI“ > „Datum Uhrzeit“ Die Umschaltung zwischen Sommer- und Winterzeit ist bei Bedarf in Windows einzustellen. Soll ein Zeitserver verwendet werden, ist die URL des Servers ebenfalls unter Windows zu projizieren. ## 3.9.4.2 Maschinen mit SINUMERIK Operate auf NCU Die Einstellung von Datum und Uhrzeit erfolgt unter: „IBN“ > „HMI“ > „Datum Uhrzeit“ Die Umschaltung zwischen Sommer- und Winterzeit und die URL eines Zeitservers projizieren Sie ebenfalls in diesem Bild. **Hinweis** Sie finden die aktuelle Beschreibung der Parametrierung der Uhrzeitsynchronisation für das SINUMERIK System unter folgendem Link: - [SINUMERIK ONE](https://support.industry.siemens.com/cs/wwde/view/109801333) - [SINUMERIK 840D sl](https://support.industry.siemens.com/cs/wwde/view/109801207) ## 3.9.5 Maschinen auf Basis SIMATIC S7-1500 ### 3.9.5.1 HMI lite PLC und Bedieneinheit sind so zu projektierten, dass Datum und Uhrzeit synchronisiert werden. Als Basis für die Synchronisation wird die Universal Time, Coordinated (UTC) verwendet. Für eine korrekte Anzeige der Uhrzeit auf dem Bedienpanel muss die Zeitzoneneinstellung sowie die gültige Sommer-/Winterzeit der S7-1500 CPU und des Bedienpanels übereinstimmen. Bei der S7-1500 sind die Auswahl der Zeitzone sowie die Parameter der Sommerzeiteinstellung in der Gruppe „Uhrzeit“ der PLC-Eigenschaften dem jeweiligen Standort entsprechend vorzunehmen. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 26 Context: # 3 Projekthandbuch ## 01/2024 An dem Bedienpanel ist die Zeitzone in den „Date/Time Properties“ im Control Panel auszuwählen. Die Anwahl der Sommer- oder Winterzeit erfolgt ab der HMI Lite Version 8.1 durch das WinCC VB-Skript „_LTL_setSummerTime“. Dieses VB-Skript wird ein Mal pro Minute durch den Aufgabenplaner aufgerufen. Wenn keine Sommer-/Winterzeitumschaltung gewünscht ist, muss dieser Aufruf im Aufgabenplaner entfernt werden. ![SIMATIC HMI](link-to-image) **Hinweis:** Bitte sicherstellen, dass die korrekten Links und Daten in die Abbildung eingefügt werden. **Quellen:** - Solutions for Powertrain / TRANSILINE - © Siemens AG 2023 Alle Rechte vorbehalten - Differenzbeschreibung Volkswagen Group Components Global **Seite 3-12** Image Analysis: ### Comprehensive Examination of the Visual Content #### 1. Localization and Attribution - **Image 1:** Located at the top of the page. - **Image 2:** Located below Image 1. #### 2. Object Detection and Classification - **Image 1:** - **Objects:** - Computer screen displaying a software interface. - Multiple panels within the software interface. - **Key Features:** - A highlighted section showing "Date/Time Properties." - Various options and settings related to time configuration. - **Image 2:** - **Objects:** - A computer screen displaying the "SIMATIC HMI" software. - A popup dialog window. - A red arrow pointing towards the "Date/Time Properties." - **Key Features:** - The software interface contains multiple icons and options at the top. - The popup window displays date and time settings. #### 3. Scene and Activity Analysis - **Image 1:** - **Scene:** - A software interface on a computer screen is depicted, focusing on time configuration properties. - **Activities:** - A user configuring the date and time settings on an HMI (Human-Machine Interface) panel using the "Date/Time Properties" dialog. - **Image 2:** - **Scene:** - Another software interface screen with a popup window open. - **Activities:** - A user adjusting date and time settings within the "SIMATIC HMI" software, indicated by a red arrow pointing to the relevant section. #### 4. Text Analysis - **Image 1:** - No text detected within the image. - **Image 2:** - No text detected within the image. - **Text Description below the Images:** - **Seen Text:** - "An dem Bedienpanel ist die Zeitzone in den „Date/Time Properties“ im Control Panel anzuwählen. Die Anwahl der Sommer- oder Winterzeit erfolgt ab der HMI Lite Version 8.1 durch das WinCC VB-Skript „ITL_setSummerTime“." - "Dieses VB-Skript wird ein Mal pro Minute durch den Aufgabenplaner aufgerufen. Wenn keine Sommer-/Winterzeitumschaltung gewünscht ist, muss dieser Aufruf im Aufgabenplaner entfernt werden." - **Analysis:** - The description instructs users to select the time zone in the "Date/Time Properties" of the Control Panel on the HMI. It mentions using a VB script "ITL_setSummerTime" to configurate daylight saving time settings starting from HMI Lite Version 8.1. Furthermore, the script is called once per minute by the task scheduler, and if daylight saving time switching is not desired, it needs to be removed from the task scheduler. #### 5. Diagram and Chart Analysis - No diagrams or charts found within the images. #### 6. Product Analysis - **Image 2:** - **Products Depicted:** - "SIMATIC HMI" software. - **Main Features:** - User interface with multiple configurable options. - Popup window for date and time settings. - **Materials and Colors:** - Predominantly grey interface with icons and a designated blue sidebar section. #### 7. Anomaly Detection - No noticeable anomalies detected in the images. #### 8. Color Analysis - **Image 1:** - **Composition:** - Predominantly grey and white interface with blue highlights. - Neutral color scheme for software settings. - **Image 2:** - **Composition:** - Predominantly grey and white interface with a noticeable red arrow. - Neutral color scheme with an additional green bar and blue sidebar for "SIMATIC HMI." #### 9. Perspective and Composition - **Image 1:** - **Perspective:** - Standard front-facing view. - **Composition:** - The image focuses centrally on the software window, maintaining a balanced composition. - **Image 2:** - **Perspective:** - Standard front-facing view. - **Composition:** - The red arrow and popup window draw attention to specific settings within the software. #### 10. Contextual Significance - The images provide visual instructions on configuring time settings in an HMI system, supporting the textual guidance and facilitating user understanding of the time configuration process. #### 11. Metadata Analysis - No metadata available for analysis. #### 12. Graph and Trend Analysis - No graphs present in the images. #### 13. Graph Numbers - Not applicable as there are no graphs in the images. ### Additional Aspects #### Ablaufprozesse (Process Flows) - The process for setting the time zone and configuring daylight saving time using the "Date/Time Properties" and VB scripting is depicted. #### Prozessbeschreibungen (Process Descriptions) - Detailed descriptions of selecting the time zone and managing daylight saving settings in "Date/Time Properties" through the control panel and scripting. #### Typen Bezeichnung (Type Designations) - Type designations such as "HMI Lite Version 8.1" and "WinCC VB-Skript" are identified. #### Trend and Interpretation - A trend towards automated time setting and daylight saving configuration using scripts in control panel software. #### Tables - No tables included in the images. ### Conclusion - The provided images and corresponding text offer a comprehensive guide on time and date configuration within an HMI system. The visual elements complement the instructional text, making the process clear and straightforward for users. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 27 Context: # Projekt Handbuch ## 01/2024 ### 3 Projektübersicht Die Uhrzeit des Bedienpanels wird durch die S7-1500 synchronisiert. Die Einstellung wird in den Eigenschaften der integrierten Verbindung zwischen S7-1500 und HMI-Gerät vorgenommen. Diese Parametrierung wurde im HMI Lite VW Standardprojekt entsprechend vorgenommen. Die Uhrzeitsynchronisation der S7-1500 CPU sollte, wenn möglich, durch einen von VW zur Verfügung gestellten NTP-Server erfolgen. Die Parametrierung der Uhrzeitsynchronisation erfolgt in der Gruppe „Uhrzeitsynchronisation“ der Eigenschaften der _PROFINET-Schnittstelle_ [1] der S7-1500 CPU. Die IP-Adresse des am jeweiligen Standort gültigen NTP-Servers ist in der zuständigen Elektrofachabteilung zu erfragen und in der Parametrierung einzutragen. Das Aktualisierungsintervall ist auf 3600s einzustellen. ![Screenshot](path/to/image.png) **Hinweis:** Bildbeschreibung und Abbildung sind im Originaldokument enthalten. Image Analysis: ### Analysis of the Attached Visual Content #### 1. Localization and Attribution - **Number of Images:** There is a single image on the page. - **Image Number:** Image 1 #### 2. Object Detection and Classification - **Detected Objects:** - Computer screen with software interfaces. - Text blocks. - **Classification:** - The computer screen shows software interfaces likely related to engineering or industrial automation. #### 3. Scene and Activity Analysis - **Scene Description:** - The image captures a screenshot of a user interface from a software application. - It appears to be related to configuration settings in a Siemens industrial environment. - **Main Actors and Actions:** - No human actors are depicted. The primary focus is on configuring software parameters. #### 4. Text Analysis - **Detected Text:** - Multiple blocks of German text. - Specific settings and labels on the computer interface. - **Extracted Text:** (translated to English for clarity) ``` "The operating panel's time is synchronized by the S7-1500. The setting is made in the properties of the integrated connection between S7-1500 and HMI device parameterization. This parameterization was carried out in HMI Lite VW Standard project accordingly. The time synchronization of the S7-1500 CPU should, if possible, be done by an NTP server provided by VW. The parameterization of the time synchronization is done in the group 'Time Synchronization' of the property 'PROFINET Interface [X1]' of the S7-1500 CPU. The IP address of the valid NTP server at the respective location must be obtained from the responsible electrical department and entered into the parameter. The update interval is set to 3600s." ``` - **Analysis and Significance:** - The text provides detailed instructions on how to set up time synchronization for an S7-1500 CPU using an NTP server provided by VW. - It stresses the importance of acquiring the correct IP address from the electrical department. - The text explains the process within the HMI Lite VW Standard project. #### 5. Diagram and Chart Analysis - **Analyzed Diagrams:** - Two sections of the software interface are displayed. - **Description:** - The left section contains a navigation pane with hierarchical settings and configurations. - The right section shows a specific configuration window that likely corresponds to time synchronization settings. #### 6. Product Analysis - **Depicted Products:** - Software interfaces from a probable Siemens configuration tool. - **Features:** - Organized menu on the left with folders and settings. - Detailed parameter fields on the right for NTP time synchronization. - **Visual Differences:** - Different sections of the software interface are shown, addressing different parts of the configuration process. #### 8. Color Analysis - **Color Composition:** - Dominant colors are shades of gray, white, blue, and yellow, typical for software interfaces. - **Impact on Perception:** - The use of neutral colors enhances readability and reduces eye strain, which is beneficial for users configuring technical settings. #### 9. Perspective and Composition - **Perspective:** - The image is taken from a direct, straight-on perspective, which is standard for displaying screenshots. - **Composition:** - Clean and organized layout, with the navigation pane on the left and a detailed configuration screen on the right. #### 10. Contextual Significance - **Contextual Analysis:** - The image likely contributes to instructional material in a project handbook related to configuring Siemens automation equipment. - **Contribution to Overall Message:** - It visually supports the accompanying text instructions on time synchronization settings. #### Trend and Interpretation - **Identified Trends:** - The text and scene suggest a trend towards highly detailed, step-by-step configuration processes in industrial automation. - **Interpretation:** - Emphasizes the importance of proper configuration for time synchronization in maintaining system accuracy and reliability. ### Conclusion This analysis provides a comprehensive view of the configuration aspect of Siemens industrial equipment regarding time synchronization using the S7-1500 CPU and an NTP server, as explained visually and textually on the page. The clear organization of software interfaces and step-by-step instructions suggest a focus on precision and ease of use in industrial settings. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 28 Context: # 3.10 Festlegungen zu SINAMICS S120 ## Kompatibilitätseinstellung Beim SINAMICS S120, sowohl bei der Anwendung mit SINUMERIK 840D sl als auch mit CU320, ist die Topologievergleichtigkeit auf "niedrig" zu stellen. Damit wird beim Tausch einer Antriebskomponente bei der Prüfung des elektronischen Typschilds nur der Komponententyp geprüft. ## Systemaufbau Es ist je Motormodul nur ein Motor anzuschließen, bzw. je Doppel-Motormodul zwei Motoren. ## Belegung der Ein-/Ausgangsklemmen Die werkseitig eingestellten Belegungen der Ein-Ausgangsklemmen dürfen nur nach Rücksprache mit der zuständigen Elektrofachabteilung verändert werden. ## Vorgaben für den Einsatz der CU320 - Die Verwendung von DCC (Drive Control Chart) ist nicht zulässig. - Die Netzwerkeinstellungen für die Schnittstelle X127 (untere Ethernet-Schnittstelle) sind auf den Standardeinstellungen zu belassen: `169.254.11.22, 255.255.0.0 (Class B)` - Bei der Nutzung von Safety-Funktionen ist ein Abnahmeprotokoll zu übergeben. - Die Systemuhr der CU320 ist mit der Systemuhr der Steuerung zu synchronisieren. - Bei Verwendung der CU320 sind die Fehlermeldungen der CU320 sind in der Steuerung abzubilden und über das HMI-System anzuzeigen. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 29 Context: ```markdown # 3 Projekthandbuch ## 3.11 Roboteranbindung Für die Anbindung von Robotern ist Rücksprache mit der zuständigen Elektrofachabteilung zu halten. ## 3.12 Energieeffizienz **Hinweis** Es gelten die Vorgaben der einzelnen Standorte. ### EE@TRANSLINE Die Energiedatenerfassung sowie die Visualisierung an der Maschine ist gemäß dem TRANSLINE Standard auszuführen. Sie finden detaillierte Informationen hierzu im Systemhandbuch EE@TRANSLINE, das ein Bestandteil der zugrunde liegenden TRANSLINE Standardhandbuchsammlung ist. Sie finden das Systemhandbuch EE@TRANSLINE ebenfalls im Installationsordner von HMI PRO si RT. Die EE@TRANSLINE Bilder zur Energiedatenerfassung sind im HMI PRO und HMI Lite VW Standard Musterprojekt bereits integriert. ``` #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 30 Context: # 3 Projekthandbuch 01/2024 ## Für Notizen --- Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global 3-16 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 31 Context: # 4 Überblick Es gilt das Kapitel der zugrunde liegenden Solutions for Powertrain / TRANSLINE Standardhandbuchsammlung. © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global Solutions for Powertrain / TRANSLINE 4-1 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 32 Context: # Für Notizen --- ### Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 33 Context: # 5 Betriebsmitteltabelle Die Volkswagen Group Components Betriebsmittel-Freigabeliste TRANSLINE ersetzt die Komponentenliste aus der zugrunde liegenden Solution for Powertrain / TRANSLINE Standardhandbuchsammlung. ## Hinweis Auf Wunsch von Volkswagen werden die Betriebsmittel-Freigabelisten nicht mehr im Siemens-Volkswagen Powertrain Extranet zur Verfügung gestellt. Sie erhalten die Betriebsmittel-Freigabelisten über das Volkswagen Group Supply Portal oder über Ihren Ansprechpartner in der zuständigen Volkswagen-Elektrofachabteilung. ## Wichtig Es ist für CNC-basierte Maschinen das System SINUMERIK ONE oder SINUMERIK 840D sl und für PLC-basierte Maschinen das System SIMATIC S7-1500 gemäß Freigabeliste einzusetzen. Als Antriebssysteme sind SINAMICS-Antriebe gemäß Freigabeliste einzusetzen. Für die anwendungsspezifische Auswahl der Steuerung und Software-Versionen ist zwingend eine Abstimmung mit der zuständigen Elektrofachabteilung notwendig. ## Hinweis Es ist grundsätzlich das Original Siemens-Zubehör einzusetzen. Die Betriebsmittel-Freigabeliste ist bindend für alle zu liefernden Maschinen/Anlagen für neue Fertigungslinien. Bei Maschinenlieferungen für bereits bestehende Fertigungslinien (Erweiterungen) sind die einzusetzenden Komponenten gesondert mit der zuständigen Elektrofachabteilung abzustimmen und das Ergebnis ist schriftlich festzuhalten. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 34 Context: # 5 Betriebsmittel-Freigabeliste ## 01/2023 Der Einsatz von Komponenten, die nicht in der Komponentenliste enthalten sind, ist nur nach Rücksprache mit der zuständigen Elektrofachabteilung und schriftlicher Genehmigung zulässig. Gegebenenfalls muss in diesem Fall eine Ersatzteilbestellung durch den Maschinenhersteller erfolgen. --- Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 35 Context: # 6 Applikationsbeispiele Dieses Kapitel ersetzt das Kapitel „Applikationsbeispiele“ aus der zugrunde liegenden Solutions for Powertrain / TRANSLINE Standardhandbuchsammlung. ## 6.1 Mechanische Fertigung (SINUMERIK ONE) **Hinweis** Die Netzwerkdarstellung in diesem Kapitel ist nur als Prinzipdarstellung zu sehen. Es gelten die Netzwerkvorgaben der einzelnen Standorte. **Hinweis** Das Fertigungsnetz wird bauseits zur Verfügung gestellt. Das Anlagennetz ist Lieferumfang des Maschinen-/Anlagenliefers. © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global Solutions for Powertrain / TRANSLINE 6-1 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 36 Context: # 6 Applikationsbeispiele ## 6.1.1 Flexible Bearbeitungslinie ### System Diagramm ```plaintext ┌─────────────┐ │ Asservot │ │ Client │ └─────────────┘ │ │ ┌─────────────────┼─────────────────┐ │ │ │ ┌─────────────┐ ┌─────────────┐ ┌─────────────┐ │ LadenPortal │ │ Maschine 1 │ │ Maschine n │ └─────────────┘ └─────────────┘ └─────────────┘ │ │ │ └─────────────────┴─────────────────┘ │ ┌─────────────┐ │ SIMATIC │ │ S7-1500 │ └─────────────┘ │ │ ┌─────────────┐ │ PROFINET │ │ Netzwerk │ └─────────────┘ ``` ### Anmerkungen - **SMATIC S7-1500**: Steuerungsplattform - **PROFINET**: Kommunikationsstandard Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global Image Analysis: ### Comprehensive Image Analysis #### 1. **Localization and Attribution:** - **Image Location:** Single image centered on the page. This is Image 1. - **Title:** "6.1.1 Flexible Bearbeitungslinie" #### 2. **Object Detection and Classification:** - **Objects and Classification:** - **Computers/Monitors:** Displayed at the top connected to different systems (Übergeord. Systeme and Assocoto Client). - **Controllers:** SIMATIC S7-1500 and SIMARRETIC ONE SIMATIC S7-1500. - **Machines:** Three labeled sections: “Lade/Portal”, “Maschine 1”, and “Maschine n”. - **Green Lines (Connections):** Represent connections between different components labeled as "Anlagenetz (PROFINET)". #### 3. **Scene and Activity Analysis:** - **Scene Description:** - The image depicts a flexible processing line in a manufacturing or industrial setup. - It illustrates the interconnected layout of computers, controllers, and machines which are part of a production line. - **Activity:** - The components are connected through a PROFINET network, suggesting communication and data exchange across the system. #### 4. **Text Analysis:** - **Detected Text:** - **General:** - “6.1.1 Flexible Bearbeitungslinie” - “Übergeord. Systeme” - “Assocoto Client” - “Fertigungsnetz” - “Anlagenetz (PROFINET)” - **Components:** - “Lade/Portal” - “Maschine 1” - “Maschine n” - “SIMATIC S7-1500” - “SIMATIC S7-1500” - “SIMARRETIC ONE SIMATIC S7-1500” - **Significance:** - The text indicates various sections and components of a flexible machining line system, highlighting the integration of network systems (PROFINET) for efficient operations. #### 5. **Diagram and Chart Analysis:** - **Diagram Description:** - The image is a diagram illustrating process flows in a machining or manufacturing line. - **Axes, Scales, and Legends:** - No explicit axes, scales, or legends are present, but the labels on the components and connections provide contextual information. #### 8. **Color Analysis:** - **Color Composition:** - **Dominant Colors:** Blue and Green - **Impact on Perception:** - The use of blue suggests a technical and structured environment, typically used in professional or industrial settings for clarity. - Green lines indicate connectivity and network paths, emphasizing the communication links crucial for the system’s operations. #### 9. **Perspective and Composition:** - **Perspective:** - The diagram is presented from a straight-on perspective for a clear and organized view of the system layout. - **Composition:** - **Arrangement of Elements:** - Top section contains overarching computers/systems. - Middle section showcases controllers and their specific types. - Bottom three segments represent different machines/modules connected by network lines. #### 10. **Contextual Significance:** - **Overall Document/Website Context:** - Likely part of a technical manual or document explaining the configuration and operation of a flexible machining line in a Siemens/VW Group manufacturing setting. - **Contribution:** - The image visualizes the connectivity and structure of the machining line, aiding understanding of the flexible line concept and how different components interface through PROFINET. #### 12. **Graph and Trend Analysis:** - **Data and Trends:** - No explicit graphs or trends are presented beyond the layout depiction and connectivity of components. #### 13. **Tables:** - **Table Analysis:** - While there is no explicit table in the image, each labeled section (e.g., “Lade/Portal”, “Maschine 1”, “Maschine n”) can be interpreted as table-like segmentation of functions or modules within the system. ### Conclusion: This diagram provides a detailed visualization of a flexible processing line, emphasizing its interconnected structure facilitated by PROFINET networking, crucial for the efficient operation of the industrial setup. It enhances the comprehensive understanding of the system for technical and operational reference. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 37 Context: ``` # 6.1.2 Maschine oder Lader/Portal auf CNC-Basis (ohne IPC) ## Fertigungsnetz ### Anlagennetz (PROFINET) ``` PN/PN Koppler ITC 1900 MCP 1900 bzw. MPP 464 EKS HT 10 ET 200pro ET 200SP 1FT7 / 1KF7 / 1PH8 ``` ## Bedienen & Beobachten - **Bedienfeld:** ITC 1900 - **Software:** HMI PRO VW Standard - **CNC:** SINUMERIK ONE NCU mit integrierter S7-1500F CPU (TIA Portal Engineering) ## Kommunikation ### PROFINET - **Zur Peripherie:** - PNIX150-Schnittstelle der SINUMERIK ONE - PNIX150-Schnittstelle der SINUMERIK ONE, mit zusätzlichem PN/PN-Koppler ### Ethernet - **Zum Bedienfeld:** - X120-Schnittstelle der SINUMERIK ONE. Hier sind ggf. auch weitere Bedienelemente anzuschließen, z. B. Anschluss-Boxen für das HT 10 oder ein EKS-Laser. - **Zum Fertigungsnetz:** - X130-Schnittstelle der SINUMERIK ONE - **Service-Schnittstelle:** - X127-Schnittstelle der SINUMERIK ONE ### Dezentrale Peripherie - **Antrieb:** SINAMICS S120 - **Motoren:** 1FT7, 1KF7, 1PH8 © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global ``` Image Analysis: ### Analysis of Visual Content #### 1. Localization and Attribution - **Image Position:** There is one image located centrally on the page beneath the heading and diagram. - **Numbering:** - **Image 1:** The main diagram presented on the page. #### 2. Object Detection and Classification - **Image 1:** - **Objects Detected:** - ITC 1900 (Monitor) - MCP 1900 - EKS - HT 10 - SCALANCE Switch - SINUMERIK ONE/iFT7/iFK7/1PH8 - ET 200pro - ET 200SP - **Classification:** - Monitors/Displays: ITC 1900, MCP 1900 - Control Unit: EKS, HT 10 - Network Switches: two SCALANCE Switches - Modules: ET 200pro, ET 200SP - Other Devices: SINUMERIK ONE, SINAMICS S120 #### 3. Scene and Activity Analysis - **Scene Description:** - The diagram illustrates a system configuration for a CNC-based machine or loader/portal setup without an IPC (Industrial PC). It displays interconnected components forming part of a manufacturing network. - **Activities:** - The diagram suggests activities related to machine integration, network communication frameworks, and control system setups. #### 4. Text Analysis - **Text Detected:** - Various identification labels for devices and components. - A descriptive table listing components and their classifications, software, and connection interfaces. - **Content Significance:** - The text annotations provide identification of each component and their role within the system, including communication interfaces and specifications, essential for understanding the system layout. #### 7. Anomaly Detection - **No Anomalies Detected:** - All elements appear standard and consistent, with logical connections typical of network diagrams in industrial settings. #### 8. Color Analysis - **Dominant Colors:** - Gray: Used predominantly for device representations. - Green: Utilized for labeling network connections (PROFINET). - Blue: Indicating various device types and control unit wires. - **Impact on Perception:** - The color scheme helps differentiate between types of connections and components, enhancing clarity and ease of understanding. #### 9. Perspective and Composition - **Perspective:** - The diagram features a front-on, 2D topological view, suitable for displaying connectivity. - **Composition:** - Elements are organized logically, with labels and devices clearly demarcated to reflect their network relationship and interactions. #### 10. Contextual Significance - **Overall Context:** - This image contributes to a technical understanding for users setting up or studying CNC-based machine configurations. It gives insights into the arrangement and interface of various components and the communication pathways between them. #### 13. Graph Numbers - **Table Data Points:** (Translated for the ease of understanding) - **Operation & Observation:** - Operating Panel: ITC 1900 - Software: HMI PRO VW Standard - CNC: SINUMERIK ONE NCU with integrated S7-1500F CPU (TIA Portal Engineering) - **Communication:** - **PROFINET:** - Peripheral: PN/X150 interface of SINUMERIK ONE - Manufacturing Network: PN/X150 interface of SINUMERIK ONE with additional PN/PN coupler - **Ethernet:** - For operation panel: X120 interface of SINUMERIK ONE. - Additional connection options for HT 10 or EKS reader. - For manufacturing network: X130 SINUMERIK ONE interface - Service Interface: X127 SINUMERIK ONE interface - **Decentralized Peripheries:** - ET 200pro, ET 200SP - **Drive:** - SINAMICS S120 - **Motors:** - 1FT7, 1FK7, 1PH8 #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 38 Context: # 6.1.3 Maschine oder Lader/Portal auf CNC-Basis (mit IPC) ## Wichtig Der Einsatz des IPC427Z ist mit der zuständigen Elektrofachabteilung abzustimmen. Es ist für den IPC427Z zwingend eine wartungsfreie unterbrechungsfreie Stromversorgung gemäß Freigabeseite einzusetzen. **Fertigungsnetz:** - **Anlagennetz:** (PROFINET) ``` +-------------------------------------+ | PN-PN Koppler | +-------------------------------------+ | | +---------+ +--------+ | EKS | | SITOP | | | | UPS | +---------+ +--------+ | | | | +---------------+ +-----------+ | IPC427Z | | SINUMERIK | +---------------+ | ONE | | | | SINECTMIC S120 | +---------------+ +-----------+ ``` ### Bedienfeld & Beobachten **ITC 1900:** IPC427Z und SITOP UPS, der IPC427Z ist im Schaltschrank zu verbauen. **Software:** HMI PRO W Standard **CNC:** SINUMERIK ONE NCI mit integrierter S7-1500F CPU (TIA Portal Engineering) ### Kommunikation **PROFINET** - **zur Peripherie zum Anlagennetz:** - PNX150-Schnittstelle der SINUMERIK ONE - PNX150-Schnittstelle der SINUMERIK ONE, mit zusätzlichem PN-PN-Koppler **Ethernet** - **zum Bedienfeld:** - X120-Schnittstelle der SINUMERIK ONE. Hier sind ggf. auch weitere Bedienkomponenten anzuschließen, z. B. Anschluss-Boxen für das HT 10 oder den EKS-Leser. - X130-Schnittstelle der SINUMERIK ONE, X1-Schnittstelle des IPC427Z Image Analysis: **Localization and Attribution:** - The page presents a set of machine and equipment configurations along with related information. **Object Detection and Classification:** - **Image 1 (Equipment Diagram)**: - Various machinery and electronic equipment are depicted. - Key objects include: ITC 1900, SITOP UPS, EKS, ICP 427E, MCP 1900(MPP 464), HT 10, SCALANCE Switch, SINUMERIK ONE SINAMICS S120, and ET 200SP. **Scene and Activity Analysis:** - The scene shows a technical diagram illustrating the connection setup of various industrial control components in a production setup. The diagram also includes network lines (PROFINET) linking different components. **Text Analysis:** - The text provides instructions and technical details related to: - **Title**: "Maschine oder Lader/Portal auf CNC-Basis (mit IPC)" - **Important Notice**: The IPC427E must be coordinated with the responsible electro-technical department and connected to a maintenance-free uninterruptible power supply according to the release page. - **Details on Components**: - **Operators & Observers**: Specifications on ITC 1900, IPC427E, SITOP UPS, and other components. - **Software**: HMI PRO WV Standard. - **CNC**: SINUMERIK ONE NCU. - **Communication**: - **PROFINET**: Describes connections to periphery and devices. - **Ethernet**: Describes connections to control panels and production networks. **Diagram and Chart Analysis:** - The diagram is a network layout showing the interconnections between different industrial machinery and their respective communication links. - Key insights: - The communication between machines is primarily linked through PROFINET and Ethernet connections. - The SITOP UPS is essential for ensuring power continuity. **Ablaufprozesse (Process Flows):** - The document outlines the workflow of setting up and managing the IPC427E with the SINUMERIK ONE system. It is significant as it ensures that power and data connections are properly configured and uninterrupted. **Color Analysis:** - The image predominantly uses grayscale for the main components and green lines to indicate the network connections. This color scheme guides the reader's focus on the connectivity pathways and emphasizes the importance of network configurations. **Perspective and Composition:** - The diagram is presented in a top-down schematic view typical for technical drawings. The equipment is spatially organized to show the positioning of each device and its respective connections clearly. **Contextual Significance:** - In the context of an operational manual, this image serves to guide technicians in setting up and connecting various industrial control components correctly. It illustrates the network layout and configuration essential for the proper functioning of a CNC-based machine or loader/portal with an IPC. **Prozessbeschreibungen (Process Descriptions):** - The text describes the process for setting up the equipment, particularly the IPC427E system. This is critical for ensuring reliable and uninterrupted power supply management. **Typen Bezeichnung (Type Designations):** - The document specifies type designations such as IPC427E, SITOP UPS, ITC 1900, etc. These categories help in identifying and distinguishing between different components and their roles in the setup. **Trend and Interpretation:** - The trend shows a focus on ensuring robust connectivity and power supply for industrial automation systems. The emphasis on network configurations suggests an importance placed on integration and reliability. **Tables:** - The table at the bottom of the page provides detailed specifications and descriptions of how each component should be used and connected. This includes details on what each component is for and where it should be installed. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 39 Context: ```markdown # 6 Applikationsbeispiele ### 6.1.4 Maschine oder Lader/Portal auf PLC-Basis #### Fertigungsnetz **Anlagennetz (PROFINET)** ``` +-----------------------+ | SIMATIC | | S7-1500 | +-----------------------+ | x1 | +------------------+------------------+ | | +-------+-------+ +------+-------+ | SCALANCE | | PN-PN | | Switch | | Koppler | +------------------+ +--------------+ | x2 | +------v-------+ | MTP1200 Comfort | | TP1200 Comfort Panel | +-----------------------------+ | +-----------------+--------------------+ | | +------v-------+ +-----+-------+ | ET 200pro | | ET 200SP | | | | | +--------------+ +-------------+ | RF 18C | +--------------------------------------+ ``` ### Bedienen & Beobachten - **Bedienfeld** - TP1200 Comfort Panel mit HMI Live Vt Standard - MTP1200 Unified Comfort Panel mit Create MyHMI / Automotive ### PLC - **SIMATIC S7-1500F** ### Kommunikation - **Zur Peripherie** - Integrierte X1-Schnittstelle der CPU - Hier ist ggf. auch der EKS-Leser anzuschließen und in das S7-1500-Programm einzubinden. - Integrierte X1-Schnittstelle der CPU - **Zum Bedienfeld** - Integrierte X1-Schnittstelle der CPU © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global ``` Image Analysis: **Image Analysis** ### 1. Localization and Attribution - **Image Positioning**: The image is positioned in the top central portion of the page. - **Image Number**: Image 1 ### 2. Object Detection and Classification - **Objects Identified**: - Multiple electronic components and network elements as well as text boxes and flow lines including: - ET 200pro, ET 200SP modules - SINAMICS S120 modules - SIMATIC S7-1500 controller - SCALANCE Switch - RF180C - PN/PN Coupler - HMI panels (MTP1200 Comfort, TP1200 Comfort) - Key text boxes such as the component list at the top and operational instructions at the bottom. ### 3. Scene and Activity Analysis - **Scene Description**: This is a technical diagram of a manufacturing network setup showing various interconnected components used in a Profinet system. - **Main Actors and Actions**: - **Main Actors**: Electronic components like controllers, switches, and HMI panels. - **Actions**: Data flow and communication connections between devices are illustrated. ### 4. Text Analysis - **Text Extracted**: - Table at the top specifying: - "Serviceschnittstelle: X127-Schnittstelle der SINUMERIK ONE" - "Dezentrale Peripherie: ET 200pro, ET 200SP" - "Antrieb: SINAMICS S120" - "Motoren: 1FT7, 1FK7, 1PH8" - Below the diagram: - Title: "6.1.4 Maschine oder Lader/Portal auf PLC-Basis" - Bedienen & Beobachten: TP1200 Comfort Panel mit HMI Lite VW Standard, MTP1200 Unified Comfort Panel mit Create MyHMI/Automotive - PLC: SIMATIC S7-1500F - Kommunikation: Details of integrated X1 interfaces and connection guidelines ### 5. Diagram and Chart Analysis - **Diagram Analysis**: - The diagram represents a network layout of industrial automation components linked by Profinet. - **Axes and Scales**: Not applicable as this is not a typical chart. - **Legend**: No explicit legend, but devices are labeled for identification. ### 6. Product Analysis - **Products Depicted**: - Various Siemens automation products including PLCs, HMI panels, and SINAMICS drives. - Key Features: Control and automation functionality for manufacturing processes, various interfaces for communication. - Materials and Colors: Typically industrial-grade materials, standard Siemens device colors (gray and blue shades). ### 7. Anomaly Detection - **Anomalies Identified**: No apparent anomalies are visible in the diagram. ### 8. Color Analysis - **Dominant Colors**: - Green for Profinet connections. - Light blue and gray for electronic components. - These colors guide the viewer in distinguishing between different types of connections and hardware elements. ### 9. Perspective and Composition - **Perspective**: The diagram is a frontal view of interconnected components. - **Composition**: It is structured to show the hierarchical connection between devices from the network infrastructure top to the user interfaces. ### 10. Contextual Significance - **Overall Document/Website Contribution**: - This image serves as a technical illustration in a manual or guide related to setting up industrial automation networks using Siemens products. - It clarifies the placement and connection of different components in a manufacturing environment. ### 11. Metadata Analysis - **Available Metadata**: - Document Date: 01/2024 - Page Number: 6-5 - Copyright: Siemens AG 2023 - Non-availability of image capture details since this is a schematic drawing. ### 12. Graph and Trend Analysis - **Analysis**: Not applicable as this section is depicting a network diagram rather than traditional graph data. ### Additional Technical Content - **Ablaufprozesse (Process Flows)**: - The process depicted involves the communication flow from a central controller (SIMATIC S7-1500) to various peripherals including HMI panels and drive modules. - **Prozessbeschreibungen (Process Descriptions)**: - Description of inter-device communication via a Profinet network, detailing devices like TP1200 and MTP1200 HMI panels interfacing with PLC and drive modules. This detailed analysis covers the visual, textual, and technical elements presented in the image, focusing on a clear depiction of industrial communication network setups. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 40 Context: # 6 Applikationsbeispiele ## 01/2024 ### 6.2 Mechanische Fertigung (SINUMERIK 840D sl) **Hinweis** Die Netzwerkdarstellung in diesem Kapitel ist nur als Prinzipdarstellung zu sehen. Es gelten die Netzwerkvorgaben der einzelnen Standorte. **Hinweis** Das Fertigungsnetz wird basierend zur Verfügung gestellt. Das Anlagennetz ist Lieferumfang des Maschinen-/Anlagenlieferanten. ### 6.2.1 Flexible Bearbeitungslinie | **Zum Anlagennetz** | mit zusätzlichem PN/PN-Koppler | |-------------------------------|----------------------------------------| | **Zum Fertigungsnetz** | | | **Dezentrale Peripherie** | ET 200Pro, EF 200SP | | **Identitätsystem** | RF 18c, RF 30 | | **Antrieb** | SINAMICS S120 mit CU320 | | **Motoren** | 1FT7, 1FK7 | **Fertigungsgeschichte** ![Flexible Bearbeitungslinie](image_url_placeholder) - **Laden-Portal** - **Maschine 1** - **Maschine n** **Übergeordnete Systeme** - **Asynchron-Client** - **PN/PN-Koppler** - **PN/PN-Koppler** Solutions for Powertrain / TRANSLINE © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global 6-6 Image Analysis: ### Comprehensive Examination of the Attached Visual Content #### 1. **Localization and Attribution:** - **Image Number and Position:** - There is a single image on the page. - This image can be referred to as **Image 1**. #### 2. **Object Detection and Classification:** - **Image 1:** - **Objects Identified:** - Overgeord. Systeme (Overarching Systems) - Auswerte-Client - Maschinen (Machines) labeled Laden/Portal, Maschine 1, Maschine n - SIMATIC S7-1500 - SINUMERIK 840D sl (SINAMICS S120) #### 3. **Scene and Activity Analysis:** - **Image 1:** - **Scene Description:** The image depicts a network diagram related to "Mechanische Fertigung" (Mechanical Manufacturing) specifically for a "Flexible Bearbeitungslinie" (Flexible Processing Line). - **Activities:** The diagram shows the flow and connections between various systems and machines using PN/PN-Koppler (Connectors) and a PROFInet network. #### 4. **Text Analysis:** - **Detected Text:** - "Zum Anlagennetz" - "Zum Fertigungsnetz" - "Dezentrale Peripherie" - "Identsystem" - "Antrieb" - "Motoren" - "Mechanische Fertigung" - "Flexible Bearbeitungslinie" - "Hinweis" - Additional instructions and system names as specified in the image. - **Text Content Analysis:** The text specifies details about the network structure, components involved, warnings or notes (Hinweis), and describes the mechanical manufacturing process, highlighting the flexibility in the processing line setup. #### 5. **Diagram and Chart Analysis:** - **Image 1:** - **Diagram Description:** A network diagram illustrating connections between different components of a flexible processing line. - **Data and Trends:** - The diagram indicates that the manufacturing network includes decentralized peripherals, identification systems, drives, and motors. - PROFInet network is used for communication, showing the interconnection between machines and overarching systems. #### 6. **Product Analysis:** - **Products Depicted:** - **SIMATIC S7-1500:** Described as high-performance PLCs used in automation. - **SINUMERIK 840D sl:** Advanced CNC systems for controlling machine tools in automated manufacturing. - Components like PN-PN-Koppler for network interfacing. - **Features and Colors:** - The components are presented in blue and grey with simple, clean lines to denote technical and manufacturing equipment. #### 7. **Anomaly Detection:** - No anomalies are detected in the image. All elements appear to be logically placed and appropriate for a network diagram. #### 8. **Color Analysis:** - **Dominant Colors:** - Blue and green are dominant, standing out against a grey background. - Blue represents key hardware components (SIMATIC and SINUMERIK systems). - Green is used to show network connections (PROFINET). #### 9. **Perspective and Composition:** - **Perspective:** - The perspective is a straightforward, top-down view typical of network diagrams. - **Composition:** - The diagram is composed to clearly show the network flow from the overarching systems through to individual machines. - Components and connections are arranged logically to illustrate connectivity and data flow. #### 10. **Contextual Significance:** - **Overall Message:** - The diagram is part of documentation for a manufacturing setup, providing a visual representation of the network infrastructure for flexible mechanical processing lines. It helps users understand the system layout and connectivity. ### Additional Aspects: #### **Ablaufprozesse (Process Flows):** - **Process Flow Description:** - The image describes a process flow for network connectivity in a flexible manufacturing line, showing the data flow through interconnecting systems and machinery. #### **Prozessbeschreibungen (Process Descriptions):** - **Process Description:** - Detailed steps and components are shown for setting up a mechanical manufacturing line using specific systems and interfaces. ### Conclusion: The visual content comprehensively details a flexible processing line within a mechanical manufacturing network, outlining the connections, systems, and peripherals involved. The color scheme and layout effectively communicate the setup, while the accompanying text provides essential context and technical specifics. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 41 Context: # 6.2.2 Maschine oder Lader/Portal auf CNC-Basis (ohne IPC) ## Fertigungsnetz **Anlagennetz:** PROFINET ![CNC Basis Diagramm](image_path_here) ## Bedienen & Beobachten - **Bedienfeld:** - OP 012TCU oder OP 015 Black - HMI PRO VW Standard - **CNC:** - SINUMERIK 840D sl NCU mit integrierter S7-300 CPU (Classic Engineering) ## Kommunikation ### PROFINET - **Zur Peripherie zum Anlagennetz:** - PNX150-Schnittstelle der SINUMERIK 840D sl - PNX150-Schnittstelle der SINUMERIK 840D sl mit zusätzlichem PN-PN-Koppler ### Ethernet - **Zum Bedienfeld:** - X120-Schnittstelle der SINUMERIK 840D sl. Hier sind gültig auch weitere Bedienkomponenten anzuschließen, z. B. Anschluss-Boxen für das HT8 oder ein EKS-Leser. - **Zum Fertigungsnetz:** - X130-Schnittstelle der SINUMERIK 840D sl - X127-Schnittstelle der SINUMERIK 840D sl ## Dezentrale Peripherie - ET 200pro - ET 200SP ## Antrieb - SINAMICS S120 ## Motoren - 1FT7, 1FK7, 1PH8 © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global Image Analysis: ### Comprehensive Examination #### Localization and Attribution: - **Image Numbering:** - **Image 1:** Entire diagram illustrating the machine or loader/portal system on a CNC basis (without IPC) along with the associated textual elements and tables. #### Object Detection and Classification: - **Image 1:** - **Objects in the Diagram:** 1. **PN-PN Koppler:** This object is a coupling device connecting different network segments. 2. **SINUMERIK Operator Panel:** A control panel interface for the SINUMERIK system. 3. **SIPLUS ET 200pro (ET 200pro, ET 200SP):** Distributed IO modules. 4. **SCALANCE Switch:** Various types of network switches, denoted as X108, X120, PN/X150. 5. **PLC Units (1FT7, 1FK7, 1PH8):** These are motors. 6. **SINAMICS S120:** This is the drive controller unit. 7. **SINUMERIK 840D sl; SINAMICS S120:** These are the main controllers. - **Key Features:** - Interfaces and connections are represented with lines indicating PROFINET and Ethernet communication paths. #### Scene and Activity Analysis: - **Image 1:** - **Scene Description:** - The image portrays a networked system for a machine or loader/portal controlled by a CNC system without IPC. Components are interconnected showing a typical setup for industrial automation. - **Activities:** - Data flow and communication between various control and peripheral units through PROFINET and Ethernet networks. - Monitoring and control operations managed via the SINUMERIK operator panel. #### Text Analysis: - **Image 1:** - **Detected Texts & Their Content:** - Titles such as "Maschine oder Lader/Portal auf CNC-Basis (ohne IPC)" indicating the system type. - Components names and specifications e.g., "PN-PN Koppler," "SINUMERIK Operator Panel," and types of switches and motors. - Descriptions under "Bedienen & Beobachten," and "Kommunikation" outline control software and communication interfaces. - **Significance in Context:** - Provides detailed specification and interconnection required for setting up a machine or loader/portal on a CNC basis without IPC. Helps in understanding the hardware and software requirements. #### Diagram and Chart Analysis: - **Image 1:** - **Diagram Analysis:** - It shows the configuration of various elements involved in the CNC based system. - Networking through PROFINET and Ethernet for communication between different components is illustrated. - Tables give a summary of operational components and communication interfaces. #### Product Analysis: - **Image 1:** - **Product Details:** - SINUMERIK operator panel, SCALANCE Switches, and SINAMICS S120 drive controller. - Distributed IO modules and motors. - **Differences:** - The switches are different categories based on specifications denoted as X108, X120, and PN/X150. - Various motor types mentioned are 1FT7, 1FK7, and 1PH8, indicating different specs. #### Anomaly Detection: - **Image 1:** - **Anomalies:** - No noticeable anomalies as the diagram seems well-structured for its purpose. #### Color Analysis: - **Image 1:** - **Color Composition:** - Predominantly uses blue and green colors for components and connection lines, which is typical for engineering and technical diagrams. - Blue is used majorly for machines and control units, green lines indicate networking (PROFINET). #### Perspective and Composition: - **Image 1:** - **Perspective:** - Top-down perspective providing an overview of the interconnected system. - **Composition:** - Components are centrally aligned with connection paths clearly marked. Tables are aligned at the bottom for easy reference. #### Contextual Significance: - **Image 1:** - Shows the operational setting and configuration for CNC-based systems. - Assists technicians and engineers in understanding the specific layout and interconnections of components. #### Tables: - **Image 1:** - **Content of Tables:** - Operational components and their abbreviations. - Communication specifications denoted under PROFINET and Ethernet. - Peripheral device details and drive system specifications. Each element of the image assists in understanding the technical requirements and configuration setup, ensuring comprehensive knowledge for implementing a CNC-based machine or loader/portal system without IPC. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 42 Context: # 6.2.3 Maschine oder Lader/Portal auf CNC-Basis (mit IPC) **Wichtig:** Diese Konstellation kann nur mit dem Betriebssystem Windows 10 eingesetzt werden (vergl. Kap. 3.1). Der Einsatz des IPC427E ist mit der zuständigen Elektrofachabteilung abzustimmen. Es ist für den IPC427E zwingend eine wartungsfreie unterbrechungsfreie Stromversorgung gemäß Freigabeliste einzusetzen. ## Fertigungsnetz ```plaintext Anlagenbjekt (PROFINET) ``` ``` PN-PN Koppler | | +-------+---------+ | | | | SINUMERIK SCALANCE Operator Switch Panel | MCP 483 +-------+-------+ bzw. MPP 483| | | SCALANCE +-------+---------+ Switch | | IPC427E SINUMERIK 840D sl SIMATIC S120 - STOP UPS - x1 | x1 | +--------------+ | 1FT7 | 1FK7 | 1PH8 +--------------------+ | | | | ET 200pro ET 200SP ``` ## Bedienen & Beobachten **Bedienfeld:** OP 012TCI oder OP 015 Black, IPC427E und STOP UPS, der IPC427E ist im Schaltschrank zu verbauen. **Software:** HMI PRO VW Standard **CNC:** SINUMERIK 840D sl NCU mit integrierter S7-300 CPU (Classic Engineering) ## Kommunikation **PROFINET:** zur Peripherie PNX150-Schnittstelle der SINUMERIK 840D sl, PNX150-Schnittstelle der SINUMERIK 840D sl, mit zusätzlichen PN-PN-Koppler **Ethernet:** zum Bedienfeld X120-Schnittstelle der SINUMERIK 840D sl. Hier sind ggf. auch weitere Bedienkomponenten anzuschließen, z.B. Anschluss-Boxen für das HT8 oder ein EKS-Leser. Image Analysis: ### Image Analysis #### Localization and Attribution: - **Image 1:** This appears to be the only image on the page. #### Object Detection and Classification: - **Detected Objects:** - Various technical equipment and components such as: - PN/PN Koppler - SINUMERIK Operator Panel - IPC427E - SITOP UPS - SCALANCE Switch - SINUMERIK 840D sl and SINAMICS S120 - ET 200pro and ET 200SP - 1FT7 / 1FK7 / 1PH8 (likely motors or drives) - **Key Features:** - Electrical connections depicted using green lines indicating PROFINET communication paths. - Components are connected to each other showing a network topology. #### Scene and Activity Analysis: - **Scene Description:** - A schematic diagram of an industrial control system, specifically a machine loader or portal on a CNC basis with IPC (Industrial PC). - The layout describes how different equipment is interconnected for operational purposes. - **Main Activities:** - The diagram shows data flows between components, most likely for automation tasks in an industrial setup. - **Main Actors:** - Industrial PCs, Operator Panel, Communication modules, Power supplies, and Controllers. #### Text Analysis: - **Detected Text:** - Main Header: "6.2.3 Maschine oder Lader/Portal auf CNC-Basis (mit IPC)" - Warning Note: "Wichtig ... Windows 10 ... abzustimmen." - Component Descriptions: Each component is labeled with its identifier and sometimes description. - Table Text: Details about Bedienene & Beobachten (Operating & Observing) and Kommunikation (Communication). - **Text Content Significance:** - The warning note emphasizes constraints and compatibility, particularly the necessity of using Windows 10 and ensuring alignment with electrical departments. - The table provides essential details for operating the listed machine components and their communication protocols. #### Diagram and Chart Analysis: - **Diagram Description:** - The diagram illustrates a network topology of interconnected industrial components. - Green lines represent PROFINET communication. - **Data and Trends:** - Shows structured integration of components within an industrial network, emphasizing connectivity and control. #### Product Analysis: - **Product Details:** - SINUMERIK Operator Panel: Typically used for machine operation interfaces. - IPC427E: An industrial PC used for control tasks. - SINAMICS S120: A drive system for motor control. - SCALANCE Switch: A network switch for managing data flow. - SITOP UPS: An uninterruptible power supply for ensuring continuous operation. #### Anomaly Detection: - **No significant anomalies detected.** - All elements seem consistent with standard industrial automation practices. #### Color Analysis: - **Dominant Colors:** - Green: Indicates communication paths (PROFINET). - Blue and grey: Represents various devices and components. - The use of green lines helps to quickly identify data flow paths which simplifies understanding of the system layout. #### Perspective and Composition: - **Perspective:** - The image is a schematic, top-down view. - **Composition:** - Well-organized components connected through straight lines represent communication lines, making it easy to follow the network structure. #### Contextual Significance: - **Role in Document:** - Provides a detailed example of how to set up and connect various components in a CNC-based machine using specific hardware and communication protocols. - Serves as an instructional guide for technicians and engineers. #### Metadata Analysis: - **Date:** 01/2024 - **Application Examples Chapter:** 6.2.3 - This is part of an instructional document. #### Trend and Interpretation: - **Trends:** - Clear trend towards modular and interconnected industrial automation systems. #### Tables: - **Content Analysis:** - The table at the bottom lists details for "Bedienen & Beobachten" and "Kommunikation." - For Operating & Observing: Various operator control options and their respective configurations. - For Communication: Specifies PROFINET and Ethernet communication protocols and relevant interfaces for connection. ### Conclusion: The image is an informative schematic from an industrial automation guide, providing detailed instructions for setting up a CNC-based machine with an IPC, illustrating major components, their connections, and relevant communication protocols. The use of color and structured layout facilitates clear understanding and implementation. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 43 Context: | zum Fertigungsnetz | X130-Schnittstelle der SINUMERIK 840D sl | X1-Schnittstelle des IPC427E | |--------------------------------|---------------------------------------------|---------------------------------| | Service-Schnittstelle | X127-Schnittstelle der SINUMERIK 840D sl | | | Dezentrale Peripherie | ET 200pro, ET 200SP | | | Antrieb | SINAMICS S120 | | | Motoren | 1FT7, 1FK7, 1PH8 | | ## 6.2.4 Maschine oder Lader/Portal auf PLC-Basis #### Fertigungsnetz **Anlagennetz: (PROFINET)** ``` [TP1200 Comfort MTP1200 Comfort] | [PN-PN Koppler] | [SCALANCE Switch] | [SIMATIC S7-1500] [x1] | [ET 200pro] [RF 18c] | | [ET 200SP] [RF300] | [SINAMICS S120 mit CU320] [1FT7 / 1FK7] ``` ### Bedienen & Beobachten - **Bedienfeld** - TP1200 Comfort Panel mit HMI Lite VW Standard - MTP1200 Unified Comfort Panel mit Create MyHMI / Automotive - **PLC** - SIMATIC S7-1500F ### Kommunikation - **Zur Peripherie** - Integrierte X1-Schnittstelle der CPU - Hier ist ggf. auch der EKS-Laser anzuschließen und in das S7-1500-Programm einzubinden. - **Zum Bedienfeld** - Integrierte X1-Schnittstelle der CPU - Integrierte X1-Schnittstelle der CPU © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global 6-9 Image Analysis: ### Analysis: #### 1. Localization and Attribution: - **Image 1:** The entire content on the page consists of a text description with a table and a network diagram depicting a machine or loader/portal based on PLC (Programmable Logic Controller). #### 2. Object Detection and Classification: - **Image 1:** - **Objects Identified:** - Table with interface information and elements like decentralized periphery, motor drives. - Network diagram of PLC-based machine including various components such as TP1200 Comfort Panels, SIMATIC S7-1500, SCALANCE Switch, ET 200pro, ET 200SP, RF300, SINAMICS S120 drives, and motors like 1FT7, 1FK7. - **Classification:** Industrial components, automation hardware, network equipment. #### 3. Scene and Activity Analysis: - **Image 1:** - **Scene Description:** The image demonstrates a network setup and integration of PLCs in an industrial environment. - **Activities:** Automation processes involving communication between different industrial devices facilitated through various interfaces and network components. #### 4. Text Analysis: - **Extracted Text:** - Header: “6.2.4 Maschine oder Lader/Portal auf PLC-Basis” - Table Content: Interfaces for production network and service points. - Descriptions including device names and panels in the diagram. - **Significance:** The text provides necessary descriptions and naming conventions for the various elements within the industrial setup, allowing for clear understanding and reference for users implementing similar configurations. #### 5. Diagram and Chart Analysis: - **Diagram Analysis:** - **Data and Trends:** Schematic representation of network flow illustrating how different components are connected within a PLC-based automation system. - **Axes, Scales, and Legends:** Not applicable, since this isn't a graph but a network diagram. - **Key Insights:** The diagram shows integration points for different components like TP1200, SIMATIC PLC, and SCALANCE switch which are essential for ensuring smooth communication within the automation system. #### 6. Product Analysis: - **Products Depicted:** - **Main Features:** - TP1200 Comfort Panel: HMI with standard visual standards. - SIMATIC S7-1500: Central processing unit for control functions. - SCALANCE Switch: Network switch for industrial communications. - SINAMICS S120: Drives and motor controls. - **Materials and Colors:** Not specified explicitly but typically involve industrial-grade materials and standard equipment colors. - **Visual Differences:** TP1200 panels look like screens, SINAMICS S120 are represented as motor drives, the switches and PLCs as networked devices. #### 7. Anomaly Detection: - **Anomalies:** - No apparent anomalies; all elements appear well integrated to depict a coherent network layout. #### 8. Color Analysis: - **Dominant Colors:** - Green lines represent connections (likely for “Anlagennetz: PROFNET”). - Blue boxes and text indicate different devices and their connections. #### 9. Perspective and Composition: - **Perspective:** - Top-down (bird's eye) schematic representation of the networking. - **Composition:** - Organized layout with distinct separation and labeling of components, facilitating clear understanding of network flow. #### 14. Prozessbeschreibungen (Process Descriptions): - **Process Description:** - The document describes the configuration of a PLC-based automation system highlighting specific peripherals' integration into the network including communication through PROFNET, various control panels, and the use of SIMATIC systems for centralized processing and motor control. The image and text form a systematic representation of how automation components are interconnected in an industrial environment, providing a visual guide for setting up a similar PLC-based system. #################### File: Differenzbeschreibung_Volkswagen_Group_Comp_Global_01-2024.DE.pdf Page: 44 Context: # 6 Applikationsbeispiele **01/2024** ## Zum Anlagennetz - mit zusätzlichem PN/PN-Koppler - Integrierte X2-Schnittstelle der CPU ## Zum Fertigungsnetz ### Dezentrale Peripherie - ET 200pro, ET 200SP ### Identystem - RF 18c, RF 300 ### Antrieb - SINAMICS S120 mit CU320 ### Motoren - 1FT7, 1FK7 --- **Solutions for Powertrain / TRANSLINE** © Siemens AG 2023 Alle Rechte vorbehalten Differenzbeschreibung Volkswagen Group Components Global ########## """QUERY: Please summarize the whole context. It is important that you include a summary for each file. All files should be included, so please make sure to go through the entire context""" Consider the chat history for relevant information. Use all information included. Use as much tokens as needed. Important: If you find information separated by a | in the context, it is a table formatted in Markdown. Final Files Sources: VW%2010130_EN%281%29.pdf - Page 1, VW%2010130_EN%281%29.pdf - Page 3, VW%2010130_EN%281%29.pdf - Page 4, VW%2010130_EN%281%29.pdf - Page 5, VW%2010130_EN%281%29.pdf - Page 6, VW%2010130_EN%281%29.pdf - Page 7, VW%2010130_EN%281%29.pdf - Page 8, VW%2010130_EN%281%29.pdf - Page 9, VW%2010130_EN%281%29.pdf - Page 10, VW%2010130_EN%281%29.pdf - Page 11, VW%2010130_EN%281%29.pdf - Page 12, VW%2010130_EN%281%29.pdf - Page 13, VW%2010130_EN%281%29.pdf - Page 14, VW%2010130_EN%281%29.pdf - Page 15, VW%2010130_EN%281%29.pdf - Page 16, VW%2010130_EN%281%29.pdf - Page 17, VW%2010130_EN%281%29.pdf - Page 18, VW%2010130_EN%281%29.pdf - Page 19, VW%2010130_EN%281%29.pdf - Page 20, VW%2010130_EN%281%29.pdf - Page 21, VW%2010130_EN%281%29.pdf - Page 22, VW%2010130_EN%281%29.pdf - Page 23, VW%2010130_EN%281%29.pdf - Page 24, VW%2010130_EN%281%29.pdf - Page 25, VW%2010130_EN%281%29.pdf - Page 26, VW%2010130_EN%281%29.pdf - Page 27, VW%2010130_EN%281%29.pdf - Page 28, VW%2010130_EN%281%29.pdf - 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