Optimal design of one-sided exponential EWMA charts based on median run length and expected median run length

Abstract

Exponential type charts are useful tools to monitor the time between events in high-quality processes with a low defect rate. Most studies on exponential charts are designed with the average run length (ARL) metric. The only use of ARL in the design of control charts is sometimes criticized because the shape of the run length (RL) distribution of control charts changes with the shift size. In fact, the RL distribution of the exponential exponentially weighted moving average (EWMA) chart is skewed, especially when the process is in-control. Hence, the median run length (MRL) serves as a more meaningful indicator. Moreover, in some situations, the shift size in the process is unknown in advance. Under this case, the expected median run length (EMRL) can be used as the metric. In this paper, the RL properties of both the upper- and lower-sided exponential EWMA charts are studied through a Markov chain approach. Two optimal design procedures are developed for one-sided exponential EWMA charts based on the MRL and EMRL, respectively. The choices of reflecting boundaries for one-sided exponential EWMA charts are discussed through many numerical studies. The MRL and EMRL performances of the one-sided exponential EWMA charts are investigated.

Keywords:

• Exponential chart
• median run length
• expected median run length
• exponentially weighted moving average chart

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30
• 62K05

Acknowledgments

The authors are grateful to the anonymous reviewers for their useful and detailed comments which contributed to the improvement of this article.

Additional information

Funding

This work are supported by National Natural Science Foundation of China No. 71802110, Natural Science Foundation of JiangSu Province No. BK20170894, Humanity and Social Science Foundation of Ministry of Education of China No. 19YJA630061, Key Research Base of Philosophy and Social Sciences in Jiangsu-Information Industry Integration Innovation and Emergency Management Research Center.