Process Capability Analysis: Estimating Quality

285 Pages·2017·6.398 MB·English

by  Neil W. Polhemus

Process Capability
Analysis
Estimating Quality

Process Capability
Analysis
Estimating Quality
Neil W. Polhemus
©2017 by Statgraphics Technologies, Inc.
All rights reserved.
www.statgraphics.com
CRC Press
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Contents
Preface ..................................................................................xi
Acknowledgments ............................................................xiii
Author .................................................................................xv
1 Introduction .............................................................1
1.1 Relative Frequency Histogram ...................................2
1.2 Summary Statistics ......................................................6
1.2.1 Measures of Central Tendency ........................7
1.2.2 Measures of Variability ....................................9
1.2.3 Measures of Shape..........................................10
1.3 Box-and-Whisker Plot ...............................................13
1.4 Plotting Attribute Data ..............................................16
1.5 Estimating the Percentage of Nonconformities .......17
1.5.1 Proportion Nonconforming ............................18
1.5.2 Defects per Million .........................................18
1.5.3 Six Sigma and World Class Quality ...............19
1.5.4 What’s Ahead ..................................................20
References ..........................................................................22
Bibliography .......................................................................22
2 Capability Analysis Based on Proportion
of Nonconforming Items ........................................25
2.1 Estimating the Proportion of Nonconforming
Items ..........................................................................26
2.1.1 Confidence Intervals and Bounds .................27
2.1.2 Plotting the Likelihood Function ...................29
v
vi ◾ Contents
2.2 Determining Quality Levels ......................................30
2.3 Information in Zero Defects .....................................33
2.4 Incorporating Prior Information ...............................35
2.4.1 Uniform Prior ..................................................37
2.4.2 Nonuniform Prior ...........................................38
Bibliography .......................................................................41
3 Capability Analysis Based on Rate
of Nonconformities ................................................43
3.1 Estimating the Mean Nonconformities per Unit ......44
3.2 Determining Quality Levels ......................................46
3.3 Sample Size Determination.......................................49
3.4 Incorporating Prior Information ...............................50
Bibliography .......................................................................53
4 Capability Analysis of Normally Distributed Data ....55
4.1 Normal Distribution ..................................................56
4.2 Parameter Estimation ................................................57
4.3 Individuals versus Subgroup Data ...........................59
4.3.1 Levels of Variability ........................................62
4.3.2 Capability versus Performance .......................63
4.3.3 Estimating Long-Term Variability ...................63
4.3.4 Estimating Short-Term Variability from
Subgroup Data ................................................64
4.3.5 Estimating Short-Term Variability from
Individuals Data ..............................................68
4.4 Estimating the Percentage of Nonconforming Items ...70
4.5 Estimating Quality Indices ........................................72
4.5.1 Z Indices .........................................................73
4.5.2 C and P .........................................................75
p p
4.5.3 C and P .........................................................79
r r
4.5.4 C and P .......................................................80
pk pk
4.5.5 C and P .......................................................83
m m
4.5.6 C ...................................................................84
pm
4.5.7 CC .................................................................85
pk
4.5.8 K ......................................................................85
4.5.9 SQL: The Sigma Quality Level .......................86
Contents ◾ vii
4.6 Confidence Bounds for Proportion
of Nonconforming Items ..........................................88
4.6.1 Confidence Limits for One-Sided
Specifications ..................................................89
4.6.2 Confidence Limits for Two-Sided
Specifications ..................................................89
4.6.2.1 Bootstrap Confidence Limits for
Individuals Data .................................91
4.6.2.2 Bootstrap Confidence Limits for
Subgroup Data ...................................93
4.7 Summary ....................................................................93
Reference ............................................................................93
Bibliography .......................................................................94
5 Capability Analysis of Nonnormal Data .................95
5.1 Tests for Normality ....................................................96
5.2 Power Transformations .............................................99
5.2.1 Box-Cox Transformations.............................100
5.2.2 Calculating Process Capability .....................103
5.2.3 Confidence Limits for Capability Indices ....106
5.3 Fitting Alternative Distributions ..............................107
5.3.1 Selecting a Distribution ................................110
5.3.2 Testing Goodness-of-Fit ...............................116
5.3.3 Calculating Capability Indices ......................118
5.3.4 Confidence Limits for Capability Indices ....122
5.4 Nonnormal Capability Indices and Johnson
Curves .................................................................124
5.5 Comparison of Methods .........................................128
References ........................................................................129
Bibliography .....................................................................129
6 Statistical Tolerance Limits ..................................131
6.1 Tolerance Limits for Normal Distributions .............133
6.2 Tolerance Limits for Nonnormal Distributions ......136
6.2.1 Tolerance Limits Based on Power
Transformations ............................................136
viii ◾ Contents
6.2.2 Tolerance Limits Based on Alternative
Distributions ..................................................139
6.3 Nonparametric Statistical Tolerance Limits ............141
References ........................................................................143
Bibliography .....................................................................143
7 Multivariate Capability Analysis ..........................145
7.1 Visualizing Bivariate Data .......................................147
7.2 Multivariate Normal Distribution ............................149
7.3 Multivariate Tests for Normality .............................152
7.4 Multivariate Capability Indices ...............................155
7.5 Confidence Intervals ...............................................159
7.6 Multivariate Normal Statistical Tolerance Limits ....161
7.6.1 Multivariate Tolerance Regions ....................161
7.6.2 Simultaneous Tolerance Limits ....................163
7.7 Analysis of Nonnormal Multivariate Data ..............165
References ........................................................................170
Bibliography .....................................................................170
8 Sample Size Determination ..................................173
8.1 Sample Size Determination for Attribute Data ......174
8.1.1 Sample Size Determination for Proportion
of Nonconforming Items ..............................174
8.1.1.1 Specification of Error Bounds .........175
8.1.1.2 Specification of Alpha and Beta
Risks ..................................................176
8.1.2 Sample Size Determination for Rate
of Nonconformities .......................................178
8.2 Sample Size Determination for Capability Indices ...180
8.2.1 Sample Size Determination for C and P ...180
p p
8.2.2 Sample Size Determination for C
pk
and P ........................................................183
pk
8.3 Sample Size Determination for Statistical
Tolerance Limits ......................................................185
Reference ..........................................................................189
Bibliography .....................................................................189
Contents ◾ ix
9 Control Charts for Process Capability .................191
9.1 Capability Control Charts ........................................192
9.1.1 Control Chart for Proportion
of Nonconforming Items ..............................196
9.1.2 Control Chart for Rate
of Nonconformities ...................................201
9.1.3 Control Charts for C and P ........................203
p p
9.1.4 Control Charts for C and P ......................207
pk pk
9.1.5 Sample Size Determination for Capability
Control Charts ...............................................208
9.2 Acceptance Control Charts .....................................210
9.2.1 Sigma Multiple Method ................................213
9.2.2 Beta Risk Method .........................................215
Reference ..........................................................................217
Bibliography .....................................................................217
Conclusion ..................................................................219
Appendix A: Probability Distributions .......................221
Appendix B: Guide to Capability Analysis
Procedures in Statgraphics .........................................239
Index ..........................................................................259