Statistical Analysis of Profile Monitoring

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