GB/T 40681.6-2021Statistical methods in monitoring process capability and performance - Part 6: Process capability statistics for characteristics following a multivariate normal distribution (English PDF)
生产过程能力和性能监测统计方法 第6部分：多元正态过程能力分析
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Issued by
State Administration for Market Regulation, China National Standardization Administration
Level / Type
National · Recommended
Issue date
October 11, 2021
Implementation date
May 1, 2022
Scope
GB/T 40681.6-2021 is the English-translated version of 生产过程能力和性能监测统计方法 第6部分：多元正态过程能力分析.
GB/T 40681.6-2021 is the Chinese standard "Statistical methods in monitoring process capability and performance - Part 6: Process capability statistics for characteristics following a multivariate normal distribution".
Its scope clause reads: This part of GB/T 40681 provides for the calculation process or product when it is necessary to consider a family of interrelated single variables.
Statistical methods for the performance and capabilities of product characteristics. This section is applicable to the process capability and performance estimation of the multivariate normal process in the common production process.
Note. For the sake of simplicity, the methods provided in this section are mostly described with the bivariate normal process as an example. For the different methods provided, this section does not evaluate the possible applications of each method in different situations.
The user can be based on Choose a more appropriate method for the actual situation. Its clauses include terms and definitions.
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Document preview — GB/T 40681.6-2021
National Standard of the People's Republic of China
- Classification
- A 41
Issued by: State Administration for Market Regulation, China National Standardization Administration
Contents
- Foreword
- Introduction
- 1 Scope
- 2 Normative references
- 3 Terms and definitions
- 4 Abbreviations
- 5 Process analysis
- 6 Evaluation of Multi-Process Capability and Performance
- 7 Calculation of process capability and process performance
- 7.1 Description of Type I and Type II Indices
- 7.2 Index setting and symbolic representation
- 7.3 Type Ic and Type IIc process capability index
- 7.4 Type IIa and Type IIb Process Capability Index
- 8 Example
- 8.1 Two-dimensional position tolerance
- 8.2 Location and size of slots
- Appendix A (informative appendix) Formula derivation
- Appendix B (informative appendix) Examples of shaft imbalance
- Appendix C (informative appendix) Examples of hole positions
- Appendix D (informative appendix) Transformation function construction
- References
1 Scope
This part of GB/T 40681 provides for the calculation process or product when it is necessary to consider a family of interrelated single variables.
Statistical methods for the performance and capabilities of product characteristics.
This section is applicable to the process capability and performance estimation of the multivariate normal process in the common production process.
Note. For the sake of simplicity, the methods provided in this section are mostly described with the bivariate normal process as an example.
For the different methods provided, this section does not evaluate the possible applications of each method in different situations. The user can be based on
Choose a more appropriate method for the actual situation.
2 Normative references
The following documents are indispensable for the application of this document. For dated reference documents, only the dated version is applicable to this document. For undated reference documents, the latest version (including all amendments) is applicable to this document.
ISO 22514-1 Statistical Methods in Process Management Capability and Performance Part 1.General Principles and Concepts (Statistical methodsinprocessmanagement-Capabilityandperformance-Part 1.Generalprinciplesandcon- cepts)
ISO 22514-2 Statistical Method Capability and Performance in Process Management Part 2.Process Capability and Performance of Time-Dependent Process Models
Performance (Statisticalmethodsinprocessmanagement-Capabilityandperformance-Part 2.Processcapa- bilityandperformanceoftime-dependentprocessmodels)
3 Terms and definitions
The following terms and definitions defined by ISO 22514-1 and ISO 22514-2 apply to this document.
3.1 Quantity
The size of a phenomenon, object or substance can be represented by a number and a reference object.
[JJF1001-2018, definition 3.1]
3.2 Multivariatequantity
Multiple distinguishable feature sets.
Note 1.The set can be represented by a d-dimensional array, that is, an ordered set composed of d elements.
Note 2.If the single variable in the set is represented by xi, where i=1,2,,d, the multivariate is represented by the vector x, and x=(x1,x2,,xd)T. Therefore, more
The variable can be regarded as the feature vector of the product. The value of the multivariate is represented by a point in the d-dimensional feature space.
Note 3.The elements in the vector are selected according to specific technical reasons.
Note 4.All single variables that make up the vector need to be measurable in the same product or object.
Note 5.If you use statistical methods to describe multiple variables, then the vector is regarded as a d-ary random vector.
Example 1.Combining x1=color, x2=quality and x3=number of failures into a vector, a single statistic can be used to evaluate process capability. This vector x
The dimension of is d=3.
GB/T 2829 | GB/T 6379.6 | GB/T 2828.2 | GB/T 40681.7 | GB/T 40681.2 | GB/T 40681.5 | […]
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This preview omits tables, figures, formulas and parts of the technical clauses. The complete document — 57 pages — is available in the English PDF.
Referenced standards
Normative references
ISO 22514
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Related Standards
GB/T 40681.7-2026 — Statistical methods in monitoring process capability and performance - Part 7: Capability of measurement processes
GB/T 40681.5-2021 — Statistical methods in monitoring process capability and performance - Part 5: Process capability estimates and performance for attributive characteristics
GB/T 40681.4-2021 — Statistical methods in monitoring process capability and performance - Part 4: Process capability estimates and performance measures
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