Statistical Analysis of Profile Monitoring

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