Statistical Analysis of Profile Monitoring

RASSOUL NOOROSSANA, PhD , is Professor of Industrial Engineering at Iran University of Science and Technology. A Certified Six Sigma Black Belt, he has published extensively in the areas of statistical quality control, engineering statistics, total quality management, and Six Sigma. ABBAS SAGHAEI, PhD, is Associate Professor of Industrial Engineering at Islamic Azad University, Iran. He currently focuses his research in the areas of statistical process control, design of experiments, and Six Sigma. AMIRHOSSEIN AMIRI, PhD , is Assistant Professor of Industrial Engineering at Shahed University, Iran. He has authored numerous papers in the areas of statistical process control and improvement, quality management and productivity, and design of experiments.

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