Frontiers in Statistical Quality Control 12

Preface

Part I: Statistical Process Control

Part II: Design of Experiments

Part III: Related Areas

To the Memory of Elart von Collani

Contents

Contributors

Part I Statistical Process Control

Phase I Distribution-Free Analysis with the R Package dfphase1

1 Introduction

2 Why Distribution-Free Methods in Phase I?

3 Distribution-Free Phase I Control Charts: A Brief Review

4 The dfphase1 Package

5 An Example

5.1 Description of the Data

5.2 Phase I Analysis

6 Conclusions

References

Assessment of Shewhart Control Chart Limits in Phase I Implementations Under Various Shift and Contamination Scenarios

1 Introduction

2 Phase I Application of Control Charts

3 x and s Control Charts

4 Phase I Simulations Using Shewhart Control Charts

5 Results of Simulations

6 MSE Optimal and Robust L Values for Phase I Charts

7 Conclusions

Appendix 1: Average Number of Iterations for the Cases of c = 8%

Appendix 2: True Alarm Percentages for the Cases of c = 8%

Appendix 3: Mean Square Errors for the Cases of c = 8%

References

New Results for Two-Sided CUSUM-Shewhart Control Charts

1 Introduction

2 One-Sided CUSUM-Shewhart Chart

2.1 Examples for One-Sided Designs

3 Two-Sided Case

3.1 Examples for Two-Sided Designs

4 Conclusions

Appendix 1: Collocation Design for More Than r=2 Intervals

Appendix 2: Two-Sided CUSUM Chart

References

Optimal Design of the Shiryaev–Roberts Chart: Give Your Shiryaev–Roberts a Headstart

1 Introduction

2 The Shiryaev–Roberts Chart, Its Properties and Optimization

3 Experimental Results

4 Concluding Remarks

References

On ARL-Unbiased Charts to Monitor the Traffic Intensityof a Single Server Queue

1 Introduction

1.1 Three Control Statistics: Xn, n and Wn

1.2 Xn and the M/G/1 System

1.3 n and the GI/M/1 System

1.4 Wn and the GI/G/1 System

1.5 On the Probability of Null Values of the Control Statistics

2 Detecting Upward and Downward Shifts in the Traffic Intensity

2.1 Three Upper One-Sided Charts for the Traffic Intensity

2.2 A Brief Review of ARL-Unbiased Charts

2.3 Deriving ARL-Unbiased Charts for the Traffic Intensity

3 Preliminary Results

3.1 M/G/1 Queueing System

3.2 GI/M/1 Queueing System

3.3 GI/G/1 Queueing System

3.4 Mixed vs. Discrete Control Statistics

4 Conclusion

Appendix

References

Risk-Adjusted Exponentially Weighted Moving Average Charting Procedure Based on Multi-Responses

1 Introduction

2 Proportional Odds Logistic Regression Model and Log Likelihood Ratio Statistic

3 Risk-Adjusted Exponentially Weighted Moving Average Charting Procedure

4 Evaluation of the Performances of Three Surgeons

5 Conclusions

Appendix 1: Proof of Theorem 1

Appendix 2: Proof of Theorem 2

Appendix 3: Average Run Length of EWMA Chart

References

A Primer on SPC and Web Data

1 Introduction

2 The Study

3 Monitoring Web Data

4 Conclusions

References

The Variable-Dimension Approach in Multivariate SPC

1 Introduction

2 The Variable-Dimension T2 (VDT2) Control Chart

3 The Double-Dimension T2 (DDT2) Control Chart

4 The Variable-Sample-Size Variable-Dimension T2 (VSSVDT2) Control Chart

5 The Variable-Dimension EWMA T2 (VDEWMA-T2) Control Chart

6 Summary

References

Distribution-Free Bivariate Monitoring of Dispersion

1 Introduction

2 Bivariate Control Charts: Monitoring Changes in Dispersion

2.1 Bivariate Dispersion Monitoring Using Data Depth

2.2 Bivariate Approach Using an Extension of the Robust Regression Approach: Outline for Univariate Distributions

2.3 Transformation to a Normal Distribution

2.4 Some Simulation Results

3 Example of Application

4 Concluding Remarks

References

Monitoring and Diagnosis of Causal Relationships Among Variables

1 Introduction

2 Outline of T2–Q Control Charts and Their Application

3 Proposals on Diagnosis

3.1 Isolation of the Unusual Variable

3.1.1 Modified Contribution Plots

3.1.2 Diagnosis of Variables by MT System

3.2 Diagnosis of Unusual Causal Relationship

4 Examination of the Proposed Method by Simulation

4.1 Simulation Models and Simulation Experiments

4.2 Comparison of Methods of Isolating Unusual Variable

4.3 Performance of the Proposed Method

5 Conclusive Remarks

References

Statistical Monitoring of Multi-Stage Processes

1 Introduction

2 Variables, Operations and Timeslides

2.1 Variables

2.2 Operations

2.3 Timeslides

3 Multi-Stage Data Flow

3.1 The Process Inputs

3.2 Outputs

4 The Detection Algorithms

4.1 One-Sided Detection Schemes

4.2 Lower and Two-Sided Detection Schemes

5 Alarm Attributes

5.1 Severity

5.2 Last Good Period

5.3 Forgiveness Criteria

6 Discussion

References

Control Charts for Time-Dependent Categorical Processes

1 Introduction

2 Modeling and Analyzing Categorical Processes

3 Sample-Based Monitoring of Categorical Processes

3.1 Sample-Based Monitoring: Binary Case

3.2 Sample-Based Monitoring: i.i.d. Case

3.3 Sample-Based Monitoring of Serially Dependent Categorical Processes

3.4 Sample-Based Monitoring: ARL Performance

4 Continuous Monitoring of Categorical Processes

4.1 Continuous Monitoring: Binary Case

4.2 Continuous Monitoring: Categorical Case

4.3 Continuous Monitoring: ARL Performance

5 Conclusions and Future Research

References

Monitoring of Short Series of Dependent ObservationsUsing a XWAM Control Chart

1 Introduction

2 Mathematical Model and the Design of an XWAM Control Chart

2.1 Introductory Remarks

2.2 Mathematical Model

2.3 Design of the XWAM Control Chart

3 Similarity Measures of Series of Observations

3.1 Introductory Remarks

3.2 Similarity Measures of Series of Observations

3.3 Construction of Prior Probabilities (Weights)

4 Numerical Experiments

4.1 Properties of X Charts and X Charts for Residuals

4.2 Properties of XWAM Charts for Residuals

5 Conclusions

References

Challenges in Monitoring Non-stationary Time Series

1 Introduction

2 Handling Non-stationary Processes

2.1 Unit Root Problems

2.2 State-Space Models

2.3 Modeling the Out-of-Control Process

3 Control Charts for Non-stationary Processes

3.1 The Transformation Approach

3.2 Control Charts with Reference Parameters for State-Space Models

3.2.1 The Likelihood Ratio Chart

3.2.2 The Sequential Probability Ratio Chart

3.2.3 The Shiryaev–Roberts Chart

3.3 Control Charts without Reference Parameters for State-Space Processes

3.3.1 The GLR Chart

3.3.2 GSPRT Chart

3.3.3 GMSR Chart

4 Comparison Study

4.1 Comparison Study Based on the Average Run Length

4.2 Comparison Study Based on the Average Delay

4.3 Robustness Study with Respect to the Choice of the Reference Value

4.4 Conclusions

5 Challenges and Problems

6 Summary

References

Part II Design of Experiments

Design of Experiments: A Key to Successful Innovation

1 Introduction

2 Innovation and Invention

3 The Scientific Method and Design of Experiments

4 The Role of Design of Experiments in Innovation

5 Barriers Hindering the Use of Design of Experiments

6 Recent Developments in Design of Experiments

7 Conclusions

References

D-Optimal Three-Stage Unbalanced Nested Designsfor the Determination of Measurement Precision

1 Introduction

2 D-Optimality for the Determination of Measurement Precision

3 D-Optimal Three-Stage Unbalanced Nested Designs

3.1 Derivation of the Optimal Designs

3.2 Sensitivity of the Generalized Variance to Sample Size n

4 Conclusions

References

Part III Related Areas

Sampling Inspection by Variables Under Weibull Distribution and Type I Censoring

1 Introduction

2 The Model

3 The Sampling Plan

4 An Example

5 A Graphical Approach

6 Conclusions

Annex A: Maximum Likelihood Estimation of the Parameters of the Gumbel Distribution

Annex B: The Variance of the Test Statistic y = - k

References

Approximate Log-Linear Cumulative Exposure Time Scale Model by Joint Moment Generating Function of Covariates

1 Time Scale Models

2 Cumulative Exposure Time Scale Model

3 Formulas for Maximum Likelihood Estimation

4 Log-Linear Cumulative Exposure Model as Approximate Accelerated Failure Time Model

5 Further Approximations of Empirical Moment Generating Function

6 Simulation Study

7 Remarks

References

A Critique of Bayesian Approaches within Quality Improvement

1 Introduction: Scientific Method—Box and Deming

2 Box and Deming

3 Basic Issues with Bayesian Methods

4 Applications of Bayesian Approaches to Process Monitoring

5 Experimental Design and Analysis

6 Final Comments

References

A Note on the Quality of Biomedical Statistics

1 Introduction

2 Laboratory Medicine

3 Evidence-Based Medicine (EbM)

4 Test of Significance

4.1 Fisher's Significance Test

4.2 Neyman-Pearson Hypotheses Test

4.3 Significance Test Versus Hypotheses Test

4.4 Modern Significance Test

4.5 The Emergence of the Modern Significance Tests

5 Conclusions

References