Incorporating Runs Rules into Hotelling's χ² Control Charts

Abstract

This paper illustrates a simple and effective method of incorporating runs rules into Hotelling χ² control charts. A Markov chain will be used to obtain a desired in-control average run length (ARL). Comparisons between the basic multivariate χ² control chart and the multivariate χ² control chart, which incorporates the various runs rules, are based on their respective ARL performances. All multivariate χ² control charts that incorporate the various runs rules have shown better ARL performance compared to the basic multivariate χ² control chart for small shifts in distance λ from the in-control mean vector μ₀ to the out-of-control mean vector μ _s . An example of the application, based on the proposed method, is also given.

Keywords:

• Runs rules
• Multivariate Hotelling's χ² control chart
• Markov chain
• Average run length (ARL)

Acknowledgments

We would like to thank the referee for his helpful suggestions and comments which helped improve the contents and style of this article.