Runs rules schemes for monitoring process variability

Abstract

To increase the sensitivity of Shewhart control charts in detecting small process shifts sensitizing rules based on runs and scans are often used in practice. Shewhart control charts supplemented with runs rules for detecting shifts in process variance have not received as much attention as their counterparts for detecting shifts in process mean. In this article, we examine the performance of simple runs rules schemes for monitoring increases and/or decreases in process variance based on the sample standard deviation. We introduce one-sided S charts that overcome the weakness of high false-alarm rates when runs rules are added to a Shewhart control chart. The average run length performance and design aspects of the charts are studied thoroughly. The performance of associated two-sided control schemes is investigated as well.

Keywords:

• average run length
• markov chain embedding technique
• optimization
• runs rules
• Shewhart control charts
• standard deviation

Acknowledgements

The authors wish to express their gratitude to the anonymous referees whose constructive suggestions and comments improved significantly the manuscript.