Statistical Analysis of Profile Monitoring

Preface ix
Contributors xi
1 Introduction to Profile Monitoring 1
Introduction, 1
1.1 Functional Relationships Qualified as Profiles, 6
1.2 Functional Relationships not Qualified as Profiles, 13
1.3 Structure of This Book, 15
References, 19
2 Simple Linear Profiles 21
Introduction, 21
2.1 Phase I Simple Linear Profile, 22
2.2 Phase II Simple Linear Profile, 53
2.3 Special Cases and an Important Application, 74
2.4 Diagnostic Statistics, 77
2.5 Violation of the Model Assumptions, 81
Appendix, 83
References, 89
3 Multiple Linear and Polynomial Profiles 93
Introduction, 93
3.1 Monitoring Multiple Linear Profiles, 94
3.2 Monitoring Polynomial Profiles, 108
References, 116
4 Binary Response Profiles 117
Introduction, 117
4.1 Model Setting and Parameter Estimation, 118
4.2 Phase I Control, 120
4.3 Phase II Monitoring, 122
4.4 Applications, 123
4.5 Conclusions, 126
References, 128
5 Parametric Nonlinear Profiles 129
Introduction, 129
5.1 Nonlinear Model Estimation, 130
5.2 Phase I Methods, 132
5.3 Phase II Methods, 142
5.4 Variance Profiles, 145
Appendix, 154
References, 155
6 Nonparametric Nonlinear Profiles 157
Introduction, 157
6.1 Model Formulation and Nonparametric Example, 159
6.2 Splines, 162
6.3 Component Analysis, 170
6.4 Wavelets, 174
References, 187
7 Multivariate Linear Profiles Monitoring 189
Introduction, 189
7.1 Monitoring Multivariate Simple Linear Profiles, 190
7.2 Monitoring Multivariate Multiple Linear Profiles, 204
References, 216
8 Statistical Process Control for Geometric Specifications 217
Introduction, 217
8.1 Examples of Geometric Feature Concerning Circularity, 221
8.2 Control Charts for Profile Monitoring, 224
8.3 Simple Approaches for Monitoring Manufactured Profiles: The Industrial Practice, 233
8.4 Performance Comparison, 237
8.5 Moving from 2D Profiles to 3D Surfaces, 245
8.6 Concluding Remarks, 249
Acknowledgments, 250
References, 250
9 Correlation and Autocorrelation in Profiles 253
Introduction, 253
9.1 Methods for WPA for Linear Models, 255
9.2 Methods for BPC for Linear Models, 257
9.3 Methods for WPA and BPC for Other (Nonlinear) Models, 258
9.4 Phase I Analysis, 259
9.5 Phase II Analysis, 262
9.6 Related Issues: Rational Subgrouping and Random Effects, 263
9.7 Discussion and Open Questions, 266
Acknowledgment, 267
References, 267
10 Nonparametric Profile Monitoring 269
Introduction, 269
10.1 Monitoring Profiles Based on Nonparametric Regression, 270
10.2 Nonparametric Profile Monitoring Using Change-Point Formulation and Adaptive Smoothing, 281
10.3 Nonparametric Profile Monitoring by Mixed-Effects Modeling, 288
Appendix A: Approximate the Distributions of Quadratic Forms Like zT Az, 299
Appendix B: The Expression of lrt,k in Model (10.8), 300
References, 301
Index 303