Process Capability Indices in Theory and Practice (Kotz)

Table of Contents

1. What is it all about?

1.1 Introduction

1.2 History

1.3 The basic structure of process capability indices

1.4 The foundation of it all: statistical methods and distributional theory

1.5 Process capability indices and the normal distribution

1.6 Capability analysis for non-normal populations: a general approach

1.7 Estimation of mu and sigma: statisticians vs. practitioners

1.8 PCI use in industy

1.9 The great debate: to use or not to use process capability indices

1.10 References

1.11 Appendix

2. The two basic, time-honored process capability indices: C_p and C_pk

2.1 Introduction

2.2 The C_p index

2.3 The C_pk index

2.4 Tying C_p and C_pk together: the k index

2.5 References

2.6 Appendix

3. First-generation modification: C_pm and its close relatives

3.1 Introduction

3.2 The loss function approach

3.3 The C_pm index

3.4 Relative loss, L_e

3.5 Appendix

4. The avalanche

4.1 Introduction

4.2 The C_pmk index

4.3 The C_jkp index

4.4 And many more ...

4.5 New indices for non-normal data

4.6 Capability indices for skewed populations using weighted variance

4.7 New indices for correlated data

4.8 Capability indices for assembly processes

4.9 References

5. The benefit (or curse) of non-normality and asymmetry and how to get rid of them when necessary

5.1 Introduction

5.2 The effects of non-normality

5.3 Data transformation and graphical techniques for assessing non-normal process capability

5.4 The most common technique in use today for non-normal capability analysis: non-normal quantile estimation, or Clement's method

5.5 Further research in non-normal capability analysis

5.6 A special non-normal case: zero-bound data

5.7 References

6. A superstructure and unified approach to process capability indices

6.1 Introduction

6.2 A promising generalization

6.3 Statistical hypothesis testing approach

6.4 Asymptotic considerations

6.5 Asymmetric tolerances

6.6 One-sided specifications

6.7 References

7. The dangerous but unavoidable area: multivariate process capability indices

7.1 Introduction

7.2 An all-purpose (omnibus) multivariate process capability index

7.3 The bivariate case

7.4 Kocherlakotas' bivariate process capability index

7.5 Examples of multivariate data

7.6 References

7.7 Appendix: Some basic facts about vectors and matrices

8. Practical issues in capability analysis

8.1 Introduction

8.2 Process capability studies

8.3 The Capability Analysis Process

8.4 References

8.5 Appendix

9. Just say yes!

9.1 Introduction

9.2 What do you do if the process is not capable?

9.3 Reluctance to use statistics

9.4 Avoiding "statistical terrorism"

9.5 References

Appendix: List of univariate PCIs

Index