Run sum control charts for the monitoring of process variability

Abstract

A two-sided run sum S control chart is proposed and its average run length performance is evaluated via a Markov chain technique. The performance of the chart is compared to several well-known control-charting procedures for the monitoring of process variability. One-sided counterparts of the proposed run sum charts are also discussed. The numerical results demonstrate an improved performance of the run sum S control charts as compared with control charts with runs rules, especially in the detection of increasing shifts in process variability. A practical guidance for the selection of the appropriate charting procedure is also given.

Keywords:

• Average extra quadratic loss
• average run length
• control charts
• Markov chain
• process variability
• run sum
• runs rules
• sample standard deviation
• statistical process control

Acknowledgements

The authors would like to thank the two anonymous reviewers for their constructive comments and for helping us to improve the content of the paper. The first author would like to express his gratitude to the University of Nantes, where this research was completed, when he was affiliated with it.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Notes on contributors

Athanasios C. Rakitzis, received his Ph.D. in Statistics from the University of Piraeus, Greece. He is currently a Lecturer at the Department of Mathematics of the University of Aegean in Greece. His research interests include statistical process control and applied probability.

Demetrios L. Antzoulakos, received his Ph.D. in Mathematics from the University of Patras, Greece. He is currently an Associate Professor at the University of Piraeus where he has been teaching since 1997. His research interests include applied probability, statistical process control and distribution theory of runs and patterns.