A phase II run sum chart for monitoring process mean and variability

ABSTRACT

This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. The numerical analysis demonstrates an improved performance of the run sum Max control chart over the usual Max chart. In addition, a numerical comparison with the Max-EWMA control chart as well as with the Max chart supplemented with runs rules, reveals that the run sum Max chart outperforms these charts in the detection of moderate to large shifts in both process parameters. Furthermore, we provide practical guidance for the selection of the appropriate charting procedure, while the use of the proposed run sum Max chart in practice is illustrated via a numerical example.

KEYWORDS:

• Average run length
• expected average run length
• Markov chain
• Max chart
• statistical process control

MSC:

• 62P30

Acknowledgements

The authors would like to thank the anonymous reviewer and the Associate Editor for their constructive comments which improved the content and the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).