Bayesian Process Monitoring, Control And Optimization

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ISBN: 9781584885443 | 1584885440
Cover: Hardcover
Copyright: 11/10/2006

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Although there are many Bayesian statistical books that focus on biostatistics and economics, there are few that address the problems faced by engineers. Bayesian Process Monitoring, Control and Optimization resolves this need, showing you how to oversee, adjust, and optimize industrial processes.Bridging the gap between application and development, this reference adopts Bayesian approaches for actual industrial practices. Divided into four parts, it begins with an introduction that discusses inferential problems and presents modern methods in Bayesian computation. The next part explains statistical process control (SPC) and examines both univariate and multivariate process monitoring techniques. Subsequent chapters present Bayesian approaches that can be used for time series data analysis and process control. The contributors include material on the Kalman filter, radar detection, and discrete part manufacturing. The last part focuses on process optimization and illustrates the application of Bayesian regression to sequential optimization, the use of Bayesian techniques for the analysis of saturated designs, and the function of predictive distributions for optimization.Written by international contributors from academia and industry, Bayesian Process Monitoring, Control and Optimization provides up-to-date applications of Bayesian processes for industrial, mechanical, electrical, and quality engineers as well as applied statisticians.

Part I Introduction to Bayesian Inference

1 An Introduction to Bayesian Inference in Process Monitoring, Control and Optimization

(44)

Enrique del Castillo and Bianca M. Colosimo

1.1 Introduction

(1)

1.2 Basics of Bayesian Inference

(7)

1.2.1 Notation

(1)

1.2.2 Goals of Bayesian Inference

(1)

1.2.3 Bayes' Theorem for Events

(1)

1.2.4 Bayes' Theorem for Densities

(2)

1.2.5 Predictivism

(1)

1.2.6 Simulation of Posterior Quantities

(1)

1.2.7 How to Simulate the Posterior Predictive Density

(1)

1.3 Choice of Prior Distribution

(4)

1.3.1 Non-Informative Priors

(1)

1.3.2 Jeffreys' Non-Informative Priors

(2)

1.3.3 Empirical Bayes Methods

(1)

1.4 Inferences on Normally Distributed Data

(11)

1.4.1 Inferences on Normally Distributed Data (Known Variance)

(1)

1.4.1.1 Analysis with a Conjugate Prior

(1)

1.4.1.2 Analysis with a Non-Informative Prior

(1)

1.4.2 Inferences on Normally Distributed Data, both Parameters Unknown

(1)

1.4.2.1 Analysis with a Conjugate Prior

(1)

1.4.2.2 Analysis with a Non-Informative Prior

(2)

1.4.3 Inferences on Multivariate Normally Distributed Data, Mean and Covariance Matrix Unknown, Conjugate Prior

(2)

1.5 Applications in Process Monitoring

(2)

1.6 Kalman Filtering from a Bayesian Viewpoint

(4)

1.7 An Application of Kalman Filtering to Process Monitoring

(1)

1.8 An Application of Kalman Filtering to Process Control

(3)

1.9 Bayesian Linear Regression and Process Optimization

(4)

1.9.1 Analysis with a Non-Informative Prior

(3)

1.9.2 Comparison of the Bayesian Predictive Approach to Frequentist Predictions in Regression

(1)

1.10 Some General References in Bayesian Statistics

(1)

Appendix

(2)

References

(3)

2 Modern Numerical Methods in Bayesian Computation

(40)

Bianca M. Colosimo and Enrique del Castillo

2.1 Introduction

(2)

2.2 Simulation-Based Approaches with Independent Samples

(5)

2.2.1 Rejection Sampling (RS)

(2)

2.2.2 Importance Sampling (IS) and Sampling Importance Resampling (SIR)

(1)

2.2.3 Sequential Importance Sampling (SIS) or Sequential Monte Carlo (SMC)

(2)

2.3 Markov Chain Monte Carlo (MCMC)

(12)

2.3.1 Metropolis-Hastings (M-H) Algorithm

(4)

2.3.2 Gibbs Sampling (GS)

(5)

2.3.3 Convergence Diagnostics in MCMC Approaches

(1)

2.3.3.1 Raftery and Lewis' Convergence Diagnostic

(1)

2.3.3.2 Geweke's Convergence Diagnostic

(1)

2.3.3.3 Gelman and Rubin's Convergence Diagnostic

(1)

2.4 Bayesian Computation in Hierarchical Models

(9)

2.4.1 Variance Components Model

(8)

Appendix: Mini-Tutorial on Win BUGS 1.4

(5)

References

(6)

Part II Process Monitoring

3 A Bayesian Approach to Statistical Process Control

(22)

Panagiotis Tsiamyrtzis and Douglas M. Hawkins

3.1 Introduction

(1)

3.2 Statistical Modeling

(5)

3.2.1 Prior Settings

(1)

3.2.2 Model Evolution

(2)

3.2.3 Approximating the Posterior

(1)

3.3 Inference

(1)

3.4 Forecasting

(1)

3.5 Making the Model Robust

(1)

3.6 Example

(4)

3.7 Conclusions

(1)

Appendix

100

(6)

References

106

(3)

4 Empirical Bayes Process Monitoring Techniques

109

(30)

Jyh-Jen Horng Shiau and Carol J. Feltz

4.1 Introduction

110

(1)

4.2 Empirical Bayes Process Monitoring for a Univariate Continuous Variable

111

(6)

4.2.1 Estimation

113

(2)

4.2.2 A Monitoring Scheme

115

(1)

4.2.3 An Example

116

(1)

4.3 Empirical Bayes Process Monitoring for a Multivariate Continuous Variable

117

(5)

4.3.1 Estimation

118

(2)

4.3.2 Monitoring Schemes

120

(1)

4.3.3 An Example

121

(1)

4.4 Empirical Bayes Process Monitoring for Pass/Fail or Other Binary Variables

122

(4)

4.4.1 Estimation

124

(2)

4.4.2 Monitoring Schemes

126

(1)

4.5 Empirical Bayes Process Monitoring for a Polytomous Discrete Variable

126

(8)

4.5.1 Estimation

129

(3)

4.5.2 Monitoring Schemes

132

(2)

4.6 Summary and Discussion

134

(1)

Appendix

135

(2)

Acknowledgements

137

(1)

References

137

(2)

5 A Bayesian Approach to Monitoring the Mean of a Multivariate Normal Process

139

(28)

Frank B. Alt

5.1 Introduction

140

(1)

5.2 Existing Multivariate Procedures

141

(1)

5.3 Bayesian Approaches

141

(10)

5.3.1 Univariate Bayesian Procedures

141

(1)

5.3.2 A Multivariate Bayesian Approach

142

(1)

5.3.3 An Initial Multivariate Bayesian Procedure (IMBP)

143

(1)

5.3.4 Different Interpretations of IMBP

144

(1)

5.3.5 Average Run Length Comparisons

144

(3)

5.3.6 A Revised Multivariate Bayesian Procedure

147

(1)

5.3.7 Average Run Length Comparisons for the RMBP

148

(1)

5.3.8 Interpretation of Out-of-Control Signals

148

(2)

5.3.9 Study of Inertia

150

(1)

5.4 Refinement of RMBP to Alleviate Inertia

151

(6)

5.4.1 Moving Window of the k Latest Observations

151

(1)

5.4.2 ARL Comparisons using Moving Window Bayesian Procedures

152

(3)

5.4.3 Study of Inertia

155

(2)

5.4.4 Drifting Process Mean Vector

157

(1)

5.5 A Revised Univariate Bayesian Procedure

157

(2)

5.6 Robustness of the Multivariate Bayesian Procedures

159

(5)

5.6.1 Elliptically Contoured Distributions

160

(1)

5.6.2 Robustness of the MBPs

160

(1)

5.6.3 Average Run Length Comparisons When Cov(X) = Σ

161

(1)

5.6.4 Average Run Length Comparisons When Cov(X) not equal to Σ and p = 2

162

(2)

5.7 Summary and Conclusions

164

(1)

Appendix

164

(1)

References

165

(2)

6 Two-Sided Bayesian X Control Charts for Short Production Runs

167

(20)

George Tagaras and George Nenes

6.1 Introduction

168

(1)

6.2 Problem Description and Formulation

169

(8)

6.2.1 Monitoring with a Standard Shewhart Chart

170

(2)

6.2.2 Monitoring with a Bayesian Chart

172

(1)

6.2.2.1 Illustrative Example

174

(3)

6.3 The Effect of State-Space Discretization on Computational Efficiency and Accuracy

177

(6)

6.3.1 Accuracy of Cost Estimation

179

(2)

6.3.2 Quality of Bayesian Control Policies Under Different State-Space Discretizations

181

(2)

6.4 The Effect of Allowable Choices for the Sample Size and Sampling Interval

183

(1)

6.5 Summary and Conclusions

184

(2)

References

186

(1)

7 Bayes' Rule of Information and Monitoring in Manufacturing Integrated Circuits

187

(28)

Spencer Graves

7.1 Introduction

188

(1)

7.2 Factoring Joint Probability and Keeping Score

189

(4)

7.3 Bayes' Rule of Information

193

(4)

7.4 Normal Prior and Posterior

197

(1)

7.5 Normal Observations

198

(2)

7.6 Bayes and the Central Limit Theorem

200

(1)

7.7 Monitoring in Manufacturing Integrated Circuits

201

(5)

7.8 Alternative Definitions of Information in Statistics

206

(1)

7.9 Summary

207

(1)

Appendix

207

(2)

References

209

(6)

Part III Process Control and Time Series Analysis

8 A Bayesian Approach to Signal Analysis of Pulse Trains

215

(30)

Melinda Hock and Refik Soyer

8.1 Introduction

216

(1)

8.2 A Hidden Markov Model for PRIs

217

(7)

8.2.1 Notation and Preliminaries

217

(2)

8.2.2 Noisy PRI Modulations and Hidden Missingness

219

(2)

8.2.3 Modeling Hidden Missingness

221

(3)

8.3 Bayesian Analysis of the HMM

224

(4)

8.3.1 Implementation of the Gibbs Sampler

225

(3)

8.4 Kalman Filter Setup for the Model

228

(7)

8.4.1 Review of Bayesian Updating in DLMs

230

(1)

8.4.2 Bayesian Analysis of the Model Using DLM Setup

231

(4)

8.5 Model Comparison

235

(3)

8.5.1 Marginal Likelihood Computation for the Model

236

(2)

8.6 Numerical Illustration

238

(3)

8.7 Conclusion

241

(1)

References

242

(3)

9 Bayesian Approaches to Process Monitoring and Process Adjustment

245

Rong Pan

9.1 Introduction

245

(2)

9.2 Bayesian Algorithm for Detecting Process Change

247

(3)

9.3 CUSUM and Bayesian Decision Making

250

(2)

9.4 Kalman Filter Approach to Process Mean Adjustment

252

(6)

9.5 Extensions to More Complex Setup Adjustment Problems

258

(1)

9.6 Integration of Process Monitoring and Process Adjustment

258

(6)

9.7 Summary

264

(1)

References

264

(5)

Part IV Process Optimization and Designed Experiments

10 A Review of Bayesian Reliability Approaches to Multiple Response Surface Optimization

269

(64)

John J. Peterson

10.1 Introduction

270

(3)

10.2 Illustration of the Posterior Predictive Approach using the Standard Multivariate Regression Model

273

(5)

10.3 Incorporation of Noise Variables

278

(3)

10.4 Bayesian Model Averaging

281

(1)

10.5 Seemingly Unrelated Regressions Model

282

(3)

10.6 The "Dual Response" Model

285

(1)

10.7 Summary and Future Possibilities

286

(2)

References

288

(3)

11 An Application of Bayesian Statistics to Sequential Empirical Optimization

291

(1)

Carlos W. Moreno

11.1 Introduction to a Typical Situation in Industrial Production

292

(1)

11.2 Process Operations and its Optimization

292

(6)

11.3 A Solution: Sequential Empirical Optimization (SEO)

298

(1)

11.4 The Ultramax Approach for SEO

299

(6)

11.4.1 General Aspects and Introduction to Bayesian Models

300

(1)

11.4.2 A Short-Cut to Calculate Bayesian Prediction Models

301

(4)

11.5 An Example

305

(2)

11.6 Summary

307

(1)

Appendix

308

(2)

References

310

(1)

12 Bayesian Estimation from Saturated Factorial Designs

311

(1)

Marta Y. Baba and Steven G. Gilmour

12.1 Introduction

311

(2)

12.2 The Model for Saturated Designs

313

(1)

12.3 Classical Analysis

313

(2)

12.4 Bayesian Estimation

315

(14)

12.4.1 Conjugate Priors

316

(3)

12.4.2 Prior as a Finite Mixture of Densities

319

(6)

12.4.3 Non-Conjugate Priors

325

(4)

12.5 Conclusions

329

(2)

References

331

(2)

Index

333

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Bayesian Process Monitoring, Control And Optimization

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