Process Capability Analysis: Estimating Quality

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Abstract: This book considers the problem of estimating the percent of nonconforming items in a process from the ground up. It examines methods based on both attribute data and variable data. For variable data, it looks at the basic techniques that were initially developed for data from normal distributions and considers how they must be modified to deal with non-normal data. The importance of capability indices and their relationship to the percent of non-conforming items is discussed, as is the use of statistical tolerance limits. Finally, the book covers an extension of univariate capability analysis to the multivariate situation, which is often ignored. Available on amazon.com

Table of contents:

Preface

Chapter 1: Introduction. 1

1.1 Relative Frequency Histogram.. 3

1.2 Summary Statistics. 4

1.2.1 Measures of central tendency. 4

1.2.2 Measures of variability. 5

1.2.3 Measures of shape. 6

1.3 Box-and-Whisker Plot 9

1.4 Plotting Attribute Data. 10

1.5 Estimating the Percentage of Nonconformities. 12

1.5.1 Proportion nonconforming. 12

1.5.2 Defects per million. 12

1.5.3 Six Sigma and World Class Quality. 13

1.5.4 What’s ahead. 14

Chapter 2: Capability Analysis Based on Proportion of Nonconforming Items. 16

2.1 Estimating the proportion of nonconforming items. 16

2.1.1 Confidence intervals and bounds. 17

2.1.2 Plotting the likelihood function. 19

2.2 Determining quality levels. 20

2.3 The information in zero defects. 22

2.4 Incorporating prior information. 25

2.4.1 Uniform prior. 26

2.4.2 Non-uniform prior. 27

Chapter 3: Capability Analysis Based on Rate of Nonconformities. 31

3.1 Estimating the mean nonconformities per unit 31

3.2 Determining quality levels. 34

3.3 Sample size determination. 35

3.4 Incorporating prior information. 36

Chapter 4: Capability Analysis of Normally Distributed Data. 40

4.1 The normal distribution. 40

4.2 Parameter estimation. 41

4.3 Individuals versus Subgroup Data. 43

4.3.1 Levels of variability. 46

4.3.2 Capability versus performance. 47

4.3.3 Estimating long-term variability. 47

4.3.4 Estimating short-term variability from subgroup data. 47

4.3.5 Estimating short-term variability from individuals data. 50

4.4 Estimating the percentage of nonconforming items. 52

4.5 Estimating quality indices. 54

4.5.1 Z-scores. 54

4.5.2 Cp/Pp 55

4.5.3 CR/PR. 59

4.5.4 Cpk/Ppk. 59

4.5.5 CM/PM... 61

4.5.6 Cpm. 61

4.5.7 CCpk 62

4.5.8 K. 63

4.5.9 SQL – The Sigma Quality Level 63

4.6 Confidence bound for proportion of nonconforming items. 65

4.6.1 Confidence limits for one-sided specifications. 65

4.6.2 Confidence limits for two-sided specifications. 66

4.7 Summary. 68

Chapter 5: Capability Analysis of Non-Normal Data. 70

5.1 Tests for Normality. 70

5.2 Power Transformations. 73

5.2.1 Box-Cox Transformations. 74

5.2.2 Calculating Process Capability. 76

5.2.3 Confidence limits for capability indices. 78

5.3 Fitting Alternative Distributions. 80

5.3.1 Selecting a Distribution. 80

5.3.2 Testing Goodness-of-Fit 85

5.3.3 Calculating Capability Indices. 87

5.3.4 Confidence Limits for Capability Indices. 90

5.4 Non-Normal Capability Indices and Johnson Curves. 91

5.5 Comparison of Methods. 94

Chapter 6: Statistical Tolerance Limits. 96

6.1 Tolerance Limits for Normal Distributions. 97

6.2 Tolerance Limits for Non-Normal Distributions. 99

6.2.1 Tolerance Limits Based on Power Transformations. 99

6.2.2 Tolerance Limits Based on Alternative Distributions. 101

6.3 Nonparametric Statistical Tolerance Limits. 103

Chapter 7: Multivariate Capability Analysis. 106

7.1 Visualizing Bivariate Data. 107

7.2 The Multivariate Normal Distribution. 109

7.3 Multivariate Tests for Normality. 112

7.4 Multivariate Capability Indices. 114

7.5 Confidence Intervals. 118

7.6 Multivariate Normal Statistical Tolerance Limits. 118

7.6.1 Multivariate Tolerance Regions. 119

7.6.2 Simultaneous Tolerance Limits. 121

7.7 Analysis of Non-Normal Multivariate Data. 123

Chapter 8: Sample Size Determination. 127

8.1 Sample Size Determination for Attribute Data. 127

8.1.1 Sample Size Determination for Proportion of Nonconforming Items. 128

8.1.2 Sample Size Determination for Rate of Nonconformities. 131

8.2 Sample Size Determination for Capability Indices. 132

8.2.1 Sample Size Determination for Cp and Pp 132

8.2.2 Sample Size Determination for Cpk and Ppk 135

8.3 Sample Size Determination for Statistical Tolerance Limits. 137

Chapter 9: Control Charts for Process Capability. 141

9.1 Capability Control Charts. 141

9.1.1 Control chart for proportion of nonconforming items. 145

9.1.2 Control chart for rate of nonconformities. 149

9.1.3 Control charts for Cp and Pp 152

9.1.4 Control charts for Cpk and Ppk 155

9.1.5 Sample size determination for capability control charts. 158

9.2 Acceptance Control Charts. 159

Appendix A: Probability Distributions. 169

Appendix B: Guide to Capability Analysis Procedures in Statgraphics. 188