Statistical Control by Monitoring and

The second edition of Statistical Control by Monitoring and Adjustment, with revised and expanded chapters, is an updated version of a classic text in the field of quality control. Practice exercises with solutions, detailed explanations of key concepts, and a clear presentation with numerous examples and computational tables demonstrate how to improve industrial efficiency by combining statistical and engineering process quality control. This book, which provides feedback methods that can be of immediate use, is ideal for graduate students studying quality control and professional quality control engineers and statisticians.

George E. P. Box, PhD,?is Ronald Aylmer Fisher Professor Emeritus of Statistics and Industrial Engineering at the University of Wisconsin–Madison.?He is a Fellow of the Royal Society of London and the American Academy of Arts and Sciences. He is an honorary Fellow and Shewart and Deming Medalist of the American Society for Quality and an honorary member of the International Statistical Institute. He is also the recipient of the Samuel S. Wilks Memorial Medal of the?American Statistical Association and the Guy Medal in Gold of the Royal Statistical Society. Dr. Box is the coauthor of Statistics for Experimenters: Design, Innovation, and Discovery, Second Edition; Response Surfaces, Mixtures, and Ridge Analyses, Second Edition; Evolutionary Operation: A Statistical Method for Process Improvements; Improving Almost Anything: Ideas and Essays, Revised Edition; Time Series Analysis: Forecasting and Control, Fourth Edition; and Bayesian Interface and Statistical Analyses, all published by Wiley. Alberto Luceño, PhD,?is Professor in the ETS de Ingenieros de Caminos at the University of Cantabria, Spain.?He is an Associate Editor of the Journal of Quality Technology and Statistical Modelling: An International Journal.?María del Carmen Paniagua-Quiñones, PhD, is Visiting Assistant Professor in the School of Industrial Engineering at Purdue University.?Her research interests include experimental design, quality productivity, and engineering management and control process improvement. She was the recipient of the Brumbaugh Award of the American Society for Quality for Best Technical Paper in 2007.

Preface	p. xi
Introduction and Revision of Some Statistical Ideas	p. 1
Necessity for Process Control	p. 1
SPC and EPC	p. 1
Process Monitoring Without a Model	p. 3
Detecting a Signal in Noise	p. 4
Measurement Data	p. 4
Two Important Characteristics of a Probability Distribution	p. 5
Normal Distribution	p. 6
Normal Distribution Defined by ¿ and ¿	p. 6
Probabilities Associated with Normal Distribution	p. 7
Estimating Mean and Standard Deviation from Data	p. 8
Combining Estimates of ¿2	p. 9
Data on Frequencies (Events): Poisson Distribution	p. 10
Normal Approximation to Poisson Distribution	p. 12
Data on Proportion Defective: Binomial Distribution	p. 12
Normal Approximation to Binomial Distribution	p. 14
Central Limit Effect	p. 15
Problems	p. 17
Standard Control Charts Under Ideal Conditions As a First Approximation	p. 21
Control Charts for Process Monitoring	p. 21
Control Chart for Measurment (Variables) Data	p. 22
Shewhart Charts for Sample Average and Range	p. 24
Shewhart Chart for Sample Range	p. 26
Process Monitoring With Control Charts for Frequencies	p. 29
Data on Frequencies (Counts): Poisson Distribution	p. 30
Common Causes and Special Causes	p. 34
For What Kinds of Data Has the c Chart Been Used?	p. 36
Quality Control Charts for Proportions: p Chart	p. 37
EWMA Chart	p. 40
Process Monitoring Using Cumulative Sums	p. 46
Specification Limits, Target Accuracy, and Process Capability	p. 53
How Successful Process Monitoring can Improve Quality	p. 56
Problems	p. 57
What Can Go Wrong and What Can We Do About It?	p. 61
Introduction	p. 61
Measurement Charts	p. 64
Need for Time Series Models	p. 65
Types of Variation	p. 65
Nonstationary Noise	p. 66
Values for constants	p. 71
Frequencies and Proportions	p. 74
Illustration	p. 76
Robustness of EWMA	p. 78
Alternative Forms of Relationships for EWMAs	p. 79
Questions	p. 79
Introduction to Forecasting and Process Dynamics	p. 81
Forecasting with an EWMA	p. 81
Forecasting Sales of Dingles	p. 82
Pete's Rule	p. 85
Effect of Changing Discount Factor	p. 86
Estimating Best Discount Factor	p. 87
Standard Deviation of Forecast Errors and Probability Limits for Forecasts	p. 88
What to Do If You Do Not Have Enough Data to Estimate ¿	p. 89
Introduction to Process Dynamics and Transfer Function	p. 89
Dynamic Systems and Transfer Funtions	p. 90
Difference Equations to Represent Dynamic Relations	p. 90
Representing Dynamics of Industrial Process	p. 96
Transfer Function Models Using Difference Equations	p. 97
Stable and Unstable Systems	p. 98
Problems	p. 100
Nonstationary Time Series Models for Process Disturbances	p. 103
Reprise	p. 103
Stationary Time Series Model in Which Successive Values Are Correlated	p. 104
Major Effects of Statistical Dependence: Illustration	p. 105
Random Walk	p. 106
How to Test a Forecasting Method	p. 107
Qualification of EWMA As a Forecast	p. 107
Understanding Time Series Behavior with Variogram	p. 110
Sticky Innovation Generating Model for Nonstationary Noise	p. 113
Robustness of EWMA for Signal Extraction	p. 118
Signal Extraction for Disturbance Model Due to Barnard	p. 118
Questions	p. 122
Problems	p. 122
Repeated-Feedback Adjustment	p. 125
Introduction to Discrete-Feedback Control	p. 125
Inadequacy of NIID Models and Other Stationary Models for Control: Reiteration	p. 125
Three Approaches to Repeated-Feedback Adjustment that Lead to Identical Conclusions	p. 126
Some History	p. 130
Adjustment Chart	p. 132
Insensitivity to Choice of G	p. 134
Compromise Value for G	p. 135
Using Smaller Value of G to Reduce Adjustment Variance ¿2x	p. 136
Robustness of Integral Control	p. 137
Effect on Adjustment of Choosing G Different from ¿0: Obtaining Equation (6.12)	p. 139
Average Reduction in Mean-Square Error Due to Adjustment for Observations Generated by IMA Model	p. 140
Questions	p. 140
Problems	p. 140
Periodic Adjustment	p. 143
Introduction	p. 143
Periodic Adjustment	p. 143
Starting Scheme for Periodic Adjustment	p. 146
Numerical Calculations for Bounded Adjustment	p. 146
Simple Device for Facilitating Bounded Adjustment	p. 150
Bounded Adjustment Seen as Process of Tracking	p. 153
Combination of Adjustment and Monitoring	p. 153
Bounded Adjustment for Series not Generated by IMA Model	p. 155
Problems	p. 160
Control of Process with Inertia	p. 163
Adjustment Depending on Last Two Output Errors	p. 163
Minimum Mean-Square Error Control of Process With First-Order Dynamics	p. 167
Schemes with Constrained Adjustment	p. 169
PI Schemes with Constrained Adjustment	p. 170
Optimal and Near-Optimal Constrained PI Schemes: Choice of P	p. 171
Choice of G For P = -0 and P = -0.25	p. 172
PI Schemes for Process With Dead Time	p. 178
Process Monitoring and Process Adjustment	p. 181
Feedback Adjustment Applied to Process in Perfect State of Control	p. 182
Using Shewhart Chart to Adjust Unstable Process	p. 182
Feedforward Control	p. 183
Equivalence of Equations for PI Control	p. 184
Effect of Errors in Adjustment	p. 184
Choices for G and P to Attain Optimal Constrained PI Control for Various Values of ¿0 and ¿0 with d0 = 0 and d0 = 1	p. 185
Questions	p. 191
Problems	p. 191
Explicit Consideration of Monetary Cost	p. 193
Introduction	p. 193
How Often Should You Take Data?	p. 197
Choosing Adjustment Schemes Directly in Terms of Costs	p. 203
Functions h(L/¿¿a) and q(L/¿¿a) in Table 9.1	p. 205
Calculation of Minimum-Cost Schemes	p. 205
Problems	p. 207
Cuscore Charts: Looking for Signals in Noise	p. 209
Introduction	p. 209
How Are Cuscore Statistics Obtained?	p. 216
Efficient Monitoring Charts	p. 219
Useful Method for Obtaining Detector When Looking for Signal in Noise Not Necessarily White Noise	p. 221
Looking for Single Spike	p. 223
Some Times Series Examples	p. 224
Likelihood, Fisher's Efficient Score, and Cuscore Statistics	p. 227
Useful Procedure for Obtaining Appropriate Cuscore Statistics	p. 230
Detector Series for IMA Model	p. 231
Problems	p. 231
Monitoring an Operating Feedback System	p. 235
Looking for Spike in Disturbance zt Subjected to Integral Control	p. 235
Looking for Exponential Signal in Disturbance Subject to Integral Control	p. 237
Monitoring Process with Inertia Represented by First-Order Dynamics	p. 238
Reconstructing Disturbance Pattern	p. 240
Derivation of Equation (11.3)	p. 240
Derivation of Equation (11.10)	p. 242
Derivation of Equation (11.14)	p. 243
Brief Review of Time Series Analysis	p. 245
Serial Dependence: Autocorrelation Function and Variogram	p. 245
Relation of Autocorrelation Function and Variogram	p. 246
Some Time Series Models	p. 247
Stationary Models	p. 247
Autoregressive Moving-Average Models	p. 250
Nonstationary Models	p. 253
IMA [or ARIMA(0, 1, 1)] Model	p. 253
Modeling Time Series Data	p. 255
Model Identification, Model Fitting, and Diagnostic Checking	p. 256
Forecasting	p. 261
Estimation with Closed-Loop Data	p. 266
Conclusion	p. 269
Other Tools for Identification of Time Series Models	p. 269
Estimation of Time Series Parameters	p. 270
Solutions to Exercises and Problems	p. 273
References and Further Reading	p. 307
Appendix Three Time Series	p. 321
Index	p. 327
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Statistical Control by Monitoring and Adjustment

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