Power guidelines for process monitoring

Abstract

We present a process for designing monitoring procedures that includes practical power guidelines. These guidelines are based upon the average run length (ARL). The specific guideline metric is the ratio of the in-control ARL (ARL_ic) to the out-of-control ARL (ARL_oc). Our recommended design process uses that ARL Ratio, in combination with the ARL_ic, ARL_oc, and ARL curve, to design effective process monitoring procedures. For adequate power, we generally recommend an ARL Ratio of 20 or more and argue that monitoring procedures with ARL Ratios less than 10 should usually be avoided. An area of caution lies between ARL Ratios of 10 and 20, allowing us to propose a stoplight type model for use in monitoring procedure design. We also discuss exceptions to these guidelines as well as a methodology to incorporate power considerations in other approaches to control chart design.

Keywords:

• average run length (ARL)
• CUSUM control chart
• power
• process monitoring Shewhart control chart

Acknowledgements

ARL values, including those in Tables 1 and 3, and Figure 2, were calculated using CUSUM software for the normal distribution by Doug Hawkins and Dave Olwell ("Cumulative Sum Control Charts and Charting for Quality Control” https://www.stat.umn.edu/cusum/), run in batch mode using a calling program written in Python by Jacob P. Davis. We thank the reviewers for insightful, helpful comments that have facilitated meaningful improvements in this work.

Additional information

Notes on contributors

Darwin J. Davis

Darwin J. Davis is an associate professor and head of Operations Management in the Department of Business Administration at the University of Delaware. He received a PhD in Operations Management from Indiana University. He has published articles on quality control, scheduling, and mathematical modeling in various journals including Journal of Quality Technology, Decision Sciences, European Journal of Operational Research, and International Journal of Production Economics.

James M. Lucas

James M. Lucas is the Principal at J. M. Lucas and Associates, a consulting firm in Statistics and Quality Management. He is a Fellow of the American Statistical Association and of the American Society for Quality and an Associate Editor of the Journal of Quality Technology and of Quality Engineering. He has over 50 publications. He authored the most cited paper in two volumes of Technometrics and in two volumes of the Journal of Quality Technology. His awards include the William G. Hunter Award, the Shewhart Medal, the Brumbaugh Award, the H. O. Hartley Award, the Ellis R. Ott Foundation Award, the Shewell Award, and the Youden Prize.

Erwin M. Saniga

Erwin M. Saniga is Dana Johnson Professor at the University of Delaware. He received a PhD in Business Administration from the Pennsylvania State University. He has published a number of articles on mathematical modeling and statistics in journals in business, engineering, statistics, and medicine.

Michael S. Saccucci

Michael S. Saccucci is Assistant Professor in Residence in the Department of Statistics at the University of Connecticut. He is a Fellow of the American Society for Quality. His awards include the Ellis R. Ott Foundation Award and the Youden Prize.