Frontiers in Statistical Quality Control 12 (eBook)

Sven Knoth studied Mathematics at the Technical Universities of Chemnitz and Novosibirsk, Russia. At the TU Chemnitz he received his diploma in 1990 and his doctorate in 1995 with a thesis on “Quasi-stationarity of CUSUM Schemes for Erlang Distributions”. After serving as a postdoc at the Department of Biostatistics, Heinrich Heine University in Düsseldorf until the end of 1996, he switched to the European University Viadrina in Frankfurt (Oder), where he completed his postdoctoral studies in 2003. From 2004 to 2009 he worked as Senior Process Engineer and SPC Coordinator at the Advanced Mask Technology Center (AMTC) in Dresden. In April 2009 he became a Professor of Computational Statistics at the Helmut Schmidt University, the University of the Federal Armed Forces in Hamburg. Sven Knoth is the author of 40 research papers on statistics. His main research areas are SPC, implementing statistical algorithms in software, and applying statistics in the engineering world. He is currently associate editor of the journal Computational Statistics.Wolfgang Schmid studied Mathematics at the University of Ulm, Germany. He received his diploma in 1982 and his doctorate in 1984 with a thesis on “Localisation of outliers in autoregressive processes”. In 1991 he completed his postdoctoral studies with a thesis on “Outlier Tests and Outlier Identification in Time Series”.  After research stays in Ulm, Trier and Stuttgart, he became a full professor of Statistics at the European University Viadrina in Frankfurt (Oder) in 1995. Wolfgang Schmid is the author of over 130 research papers on statistics. His main research areas include statistical process control, statistics in finance, and environmetrics. He is currently associate editor of Sequential Analysis and of AStA-Advances in Statistical Analysis and since 2012 President of the German Statistical Society.  

Preface 6
Part I: Statistical Process Control 6
Part II: Design of Experiments 9
Part III: Related Areas 9
To the Memory of Elart von Collani 11
Contents 12
Contributors 14
Part I Statistical Process Control 17
Phase I Distribution-Free Analysis with the R Package dfphase1 18
1 Introduction 18
2 Why Distribution-Free Methods in Phase I? 20
3 Distribution-Free Phase I Control Charts: A Brief Review 21
4 The dfphase1 Package 22
5 An Example 24
5.1 Description of the Data 24
5.2 Phase I Analysis 27
6 Conclusions 33
References 33
Assessment of Shewhart Control Chart Limits in Phase I Implementations Under Various Shift and Contamination Scenarios 35
1 Introduction 36
2 Phase I Application of Control Charts 37
3 x and s Control Charts 38
4 Phase I Simulations Using Shewhart Control Charts 39
5 Results of Simulations 41
6 MSE Optimal and Robust L Values for Phase I Charts 49
7 Conclusions 50
Appendix 1: Average Number of Iterations for the Cases of c = 8% 52
Appendix 2: True Alarm Percentages for the Cases of c = 8% 53
Appendix 3: Mean Square Errors for the Cases of c = 8% 54
References 56
New Results for Two-Sided CUSUM-Shewhart Control Charts 58
1 Introduction 58
2 One-Sided CUSUM-Shewhart Chart 59
2.1 Examples for One-Sided Designs 63
3 Two-Sided Case 66
3.1 Examples for Two-Sided Designs 69
4 Conclusions 71
Appendix 1: Collocation Design for More Than r=2 Intervals 72
Appendix 2: Two-Sided CUSUM Chart 72
References 75
Optimal Design of the Shiryaev–Roberts Chart: Give Your Shiryaev–Roberts a Headstart 77
1 Introduction 77
2 The Shiryaev–Roberts Chart, Its Properties and Optimization 79
3 Experimental Results 84
4 Concluding Remarks 93
References 96
On ARL-Unbiased Charts to Monitor the Traffic Intensityof a Single Server Queue 99
1 Introduction 100
1.1 Three Control Statistics: Xn, n and Wn 101
1.2 Xn and the M/G/1 System 101
1.3 n and the GI/M/1 System 102
1.4 Wn and the GI/G/1 System 103
1.5 On the Probability of Null Values of the Control Statistics 104
2 Detecting Upward and Downward Shifts in the Traffic Intensity 105
2.1 Three Upper One-Sided Charts for the Traffic Intensity 106
2.2 A Brief Review of ARL-Unbiased Charts 107
2.3 Deriving ARL-Unbiased Charts for the Traffic Intensity 108
3 Preliminary Results 109
3.1 M/G/1 Queueing System 111
3.2 GI/M/1 Queueing System 114
3.3 GI/G/1 Queueing System 115
3.4 Mixed vs. Discrete Control Statistics 117
4 Conclusion 119
Appendix 120
References 121
Risk-Adjusted Exponentially Weighted Moving Average Charting Procedure Based on Multi-Responses 125
1 Introduction 125
2 Proportional Odds Logistic Regression Model and Log Likelihood Ratio Statistic 127
3 Risk-Adjusted Exponentially Weighted Moving Average Charting Procedure 131
4 Evaluation of the Performances of Three Surgeons 132
5 Conclusions 136
Appendix 1: Proof of Theorem 1 136
Appendix 2: Proof of Theorem 2 140
Appendix 3: Average Run Length of EWMA Chart 142
References 142
A Primer on SPC and Web Data 144
1 Introduction 144
2 The Study 145
3 Monitoring Web Data 149
4 Conclusions 153
References 153
The Variable-Dimension Approach in Multivariate SPC 154
1 Introduction 155
2 The Variable-Dimension T2 (VDT2) Control Chart 156
3 The Double-Dimension T2 (DDT2) Control Chart 158
4 The Variable-Sample-Size Variable-Dimension T2 (VSSVDT2) Control Chart 159
5 The Variable-Dimension EWMA T2 (VDEWMA-T2) Control Chart 161
6 Summary 164
References 165
Distribution-Free Bivariate Monitoring of Dispersion 167
1 Introduction 167
2 Bivariate Control Charts: Monitoring Changes in Dispersion 169
2.1 Bivariate Dispersion Monitoring Using Data Depth 169
2.2 Bivariate Approach Using an Extension of the Robust Regression Approach: Outline for Univariate Distributions 171
2.3 Transformation to a Normal Distribution 172
2.4 Some Simulation Results 173
3 Example of Application 179
4 Concluding Remarks 183
References 183
Monitoring and Diagnosis of Causal Relationships Among Variables 185
1 Introduction 185
2 Outline of T2–Q Control Charts and Their Application 186
3 Proposals on Diagnosis 188
3.1 Isolation of the Unusual Variable 188
3.1.1 Modified Contribution Plots 188
3.1.2 Diagnosis of Variables by MT System 189
3.2 Diagnosis of Unusual Causal Relationship 190
4 Examination of the Proposed Method by Simulation 191
4.1 Simulation Models and Simulation Experiments 191
4.2 Comparison of Methods of Isolating Unusual Variable 192
4.3 Performance of the Proposed Method 193
5 Conclusive Remarks 194
References 194
Statistical Monitoring of Multi-Stage Processes 195
1 Introduction 195
2 Variables, Operations and Timeslides 197
2.1 Variables 197
2.2 Operations 198
2.3 Timeslides 198
3 Multi-Stage Data Flow 199
3.1 The Process Inputs 201
3.2 Outputs 203
4 The Detection Algorithms 207
4.1 One-Sided Detection Schemes 208
4.2 Lower and Two-Sided Detection Schemes 209
5 Alarm Attributes 211
5.1 Severity 211
5.2 Last Good Period 212
5.3 Forgiveness Criteria 214
6 Discussion 217
References 218
Control Charts for Time-Dependent Categorical Processes 220
1 Introduction 220
2 Modeling and Analyzing Categorical Processes 222
3 Sample-Based Monitoring of Categorical Processes 225
3.1 Sample-Based Monitoring: Binary Case 225
3.2 Sample-Based Monitoring: i.i.d. Case 226
3.3 Sample-Based Monitoring of Serially Dependent Categorical Processes 229
3.4 Sample-Based Monitoring: ARL Performance 231
4 Continuous Monitoring of Categorical Processes 234
4.1 Continuous Monitoring: Binary Case 234
4.2 Continuous Monitoring: Categorical Case 235
4.3 Continuous Monitoring: ARL Performance 235
5 Conclusions and Future Research 237
References 238
Monitoring of Short Series of Dependent ObservationsUsing a XWAM Control Chart 241
1 Introduction 241
2 Mathematical Model and the Design of an XWAM Control Chart 243
2.1 Introductory Remarks 243
2.2 Mathematical Model 243
2.3 Design of the XWAM Control Chart 246
3 Similarity Measures of Series of Observations 247
3.1 Introductory Remarks 247
3.2 Similarity Measures of Series of Observations 247
3.3 Construction of Prior Probabilities (Weights) 249
4 Numerical Experiments 251
4.1 Properties of X Charts and X Charts for Residuals 251
4.2 Properties of XWAM Charts for Residuals 255
5 Conclusions 262
References 262
Challenges in Monitoring Non-stationary Time Series 264
1 Introduction 264
2 Handling Non-stationary Processes 266
2.1 Unit Root Problems 266
2.2 State-Space Models 267
2.3 Modeling the Out-of-Control Process 269
3 Control Charts for Non-stationary Processes 270
3.1 The Transformation Approach 270
3.2 Control Charts with Reference Parameters for State-Space Models 270
3.2.1 The Likelihood Ratio Chart 272
3.2.2 The Sequential Probability Ratio Chart 273
3.2.3 The Shiryaev–Roberts Chart 273
3.3 Control Charts without Reference Parameters for State-Space Processes 273
3.3.1 The GLR Chart 274
3.3.2 GSPRT Chart 274
3.3.3 GMSR Chart 275
4 Comparison Study 275
4.1 Comparison Study Based on the Average Run Length 275
4.2 Comparison Study Based on the Average Delay 276
4.3 Robustness Study with Respect to the Choice of the Reference Value 277
4.4 Conclusions 278
5 Challenges and Problems 278
6 Summary 279
References 281
Part II Design of Experiments 283
Design of Experiments: A Key to Successful Innovation 284
1 Introduction 284
2 Innovation and Invention 286
3 The Scientific Method and Design of Experiments 287
4 The Role of Design of Experiments in Innovation 290
5 Barriers Hindering the Use of Design of Experiments 290
6 Recent Developments in Design of Experiments 292
7 Conclusions 294
References 295
D-Optimal Three-Stage Unbalanced Nested Designsfor the Determination of Measurement Precision 297
1 Introduction 297
2 D-Optimality for the Determination of Measurement Precision 298
3 D-Optimal Three-Stage Unbalanced Nested Designs 301
3.1 Derivation of the Optimal Designs 301
3.2 Sensitivity of the Generalized Variance to Sample Size n 302
4 Conclusions 306
References 307
Part III Related Areas 308
Sampling Inspection by Variables Under Weibull Distribution and Type I Censoring 309
1 Introduction 310
2 The Model 311
3 The Sampling Plan 312
4 An Example 316
5 A Graphical Approach 319
6 Conclusions 321
Annex A: Maximum Likelihood Estimation of the Parameters of the Gumbel Distribution 321
Annex B: The Variance of the Test Statistic y = - k 323
References 327
Approximate Log-Linear Cumulative Exposure Time Scale Model by Joint Moment Generating Function of Covariates 329
1 Time Scale Models 329
2 Cumulative Exposure Time Scale Model 331
3 Formulas for Maximum Likelihood Estimation 333
4 Log-Linear Cumulative Exposure Model as Approximate Accelerated Failure Time Model 334
5 Further Approximations of Empirical Moment Generating Function 336
6 Simulation Study 337
7 Remarks 340
References 340
A Critique of Bayesian Approaches within Quality Improvement 342
1 Introduction: Scientific Method—Box and Deming 342
2 Box and Deming 343
3 Basic Issues with Bayesian Methods 345
4 Applications of Bayesian Approaches to Process Monitoring 347
5 Experimental Design and Analysis 350
6 Final Comments 353
References 353
A Note on the Quality of Biomedical Statistics 355
1 Introduction 355
2 Laboratory Medicine 356
3 Evidence-Based Medicine (EbM) 358
4 Test of Significance 361
4.1 Fisher's Significance Test 362
4.2 Neyman-Pearson Hypotheses Test 363
4.3 Significance Test Versus Hypotheses Test 363
4.4 Modern Significance Test 364
4.5 The Emergence of the Modern Significance Tests 365
5 Conclusions 365
References 366