An ARL-unbiased design of time-between-events control charts with runs rules

Abstract

In this paper, we consider incorporating the runs rules into the cumulative quantity control (CQC) chart for monitoring time-between-events data. We propose a simple and effective procedure to design a CQC chart coupled with runs rules that can yield average run length (ARL)-unbiased performance and meet the required in-control ARL. The proposed design involves determining a relation between the upper side and lower side false alarm probabilities. A Markov chain approach is used to evaluate the ARL performance of various control schemes studied in this paper. An extensive numerical comparison shows that the proposed design approach can result in a significant reduction in ARL for detecting increases in the occurrence rate of the event in comparison with the basic CQC charts.

Keywords:

• CQC chart
• runs rules
• Markov chain

Acknowledgements

The authors would like to thank the anonymous referees for their constructive suggestions that may improve the presentation of the paper. This research was supported by the National Science Council of the Republic of China under Grant NSC 98-2221-E-155-046.