Cumulative Sum Charts and Charting for Quality Improvement

Cumulative sum (CUSUM) control charting is a valuable tool for detecting and diagnosing persistent shifts in series of readings. It is used in traditional statistical process control (SPC) settings such as manufacturing, but is also effective in settings as diverse as personnel management, econometrics, and conventional data analysis. It is an essential tool for the quality professional. This book covers CUSUMs from an application-oriented viewpoint, while also providing the essential theoretical underpinning. It is accessible to anyone with a basic statistical training, and is aimed at quality practitioners, teachers and students of quality methodologies, and people interested in analysis of time-ordered data. The text is supported by a Web site containing CUSUM software and data sets. Douglas M. Hawkins is Chair of the Department of Applied Statistics, University of Minnesota. He is a Fellow of the American Statistical Association, a Member of the International Statistical Institute and a Senior member of the American Society for Quality Control. His work on multivariate CUSUMs won him the Ellis R. Ott Award for the best paper on quality published in 1993. He has been Associate Editor of Technometrics and Journal of the American Statistical Association. David H. Olwell is Associate Professor in the Department of Mathematical Sciences at the United States Military Academy. He is a member of the American Statistical Association, the American Society for Quality Control, and the Military Operations Research Society, where his work on applications of CUSUMs to managing sexual harassment was nominated for the 1998 Barchi prize. He is Editor of Mathematica

1 Introduction. - 1. 1 Common-cause and special-cause variability. - 1. 2 Transient and persistent special causes. - 1. 3 The Shewhart and CUSUM charts. - 1. 4 Basis for the CUSUM chart for a normal mean. - 1. 5 Out-of-control distribution of the CUSUM. - 1. 6 Testing for a shift the V mask. - 1. 7 Estimation following a signal. - 1. 8 Using individual readings or rational groups. - 1. 9 The decision interval form of the CUSUM. - 1. 10 Summary. - 1. 11 Further reading. - 2 CUSUM design. - 2. 1 The choice of k and h. - 2. 2 Runs, run length, and average run length. - 2. 3 The Shewhart Xbar chart as CUSUM. - 2. 4 Summary. - 2. 5 Further reading. - 3 More about normal data. - 3. 1 In-control ARLs. - 3. 2 Out-of-control ARLs. - 3. 3 FIR CUSUMs: zero start and steady state start. - 3. 4 Controlling for the mean within a range. - 3. 5 The impact of variance shifts. - 3. 6 Combined Shewhart and CUSUM charts. - 3. 7 Effect of model departures. - 3. 8 Weighted CUSUMs. - 3. 9 Summary. - 3. 10 Further reading. - 4 Other continuous distributions. - 4. 1 The gamma family and normal variances. - 4. 2 The inverse Gaussian family. - 4. 3 Example from General Motors. - 4. 4 Comments. - 4. 5 Further reading. - 5 Discrete data. - 5. 1 Types of discrete data. - 5. 2 The graininess of the ARL function. - 5. 3 The Poisson distribution and count data. - 5. 4 The Poisson and CUSUMs. - 5. 5 Weighted Poisson CUSUMs. - 5. 6 The binomial distribution. - 5. 7 Weighted binomial CUSUMs. - 5. 8 Other discrete distributions. - 5. 9 Summary. - 5. 10 Further reading. - 6 Theoretical foundations of the CUSUM. - 6. 1 General theory. - 6. 2 The general exponential family. - 6. 3 The Markov property of CUSUMs. - 6. 4 Getting the ARL. - 6. 5 Summary. - 6. 6 Further reading. - 7 Calibration and short runs. - 7. 1 The self-starting approach. - 7. 2 The self-starting CUSUM for a normal mean. - 7. 3 Self-startingCUSUMs for gamma data. - 7. 4 Discrete data. - 7. 5 Summary. - 7. 6 Further reading. - 8 Multivariate data. - 8. 1 Outline of the multivariate normal. - 8. 2 Shewhart charting Hotelling s T2. - 8. 3 CUSUM charting various approaches. - 8. 4 Regression adjustment. - 8. 5 Choice of regression adjustment. - 8. 6 The use of several regression-adjusted variables. - 8. 7 The multivariate exponentially weighted moving average. - 8. 8 Summary. - 8. 9 Further reading. - 9 Special topics. - 9. 1 Robust CUSUMs. - 9. 2 Recursive residuals in regression. - 9. 3 Autocorrelated data. - 9. 4 Summary. - 9. 5 Further reading. - 10 Software. - 10. 1 Programs and templates. - 10. 2 Data files. - References.