Guaranteed conditional performance of the median run length based EWMA X¯ chart with unknown process parameters

Abstract

Exponentially weighted moving average (EWMA) type charts are very popular and efficient in monitoring various kind of statistics. Much researches have been done on the EWMA $\overline{X}$ chart with known process parameters. But, in practice, the process parameters used to set the control chart limits are often unknown and they need to be estimated from different Phase I samples. Moreover, because the shape of the run length distribution for the EWMA $\overline{X}$ chart changes with the mean shift, the median run length (MRL) can serve as a good alternative to evaluate the performance of the EWMA $\overline{X}$ chart. In this article, we will investigate the conditional properties of the EWMA $\overline{X}$ chart with unknown process parameters based on the MRL metric. In order to investigate the chart’s properties, the average MRL (AMRL) and the standard deviation of MRL (SDMRL) will be used together when the process parameters are unknown. To prevent too many lower in-control MRL values, the adjusted control limits of the MRL based EWMA chart are obtained by using a bootstrap type approach and the results show that the adjusted control limits can give a good tradeoff between the in-control and out-of-control MRL performances.

Keywords:

• EWMA $\overline{\mathit{X}}$ chart
• Median run length
• Estimated parameters
• Average median run length
• Standard deviation of median run length

Acknowledgments

The authors would like to acknowledge the helpful suggestions of the anonymous reviewers and the editor.

Additional information

Funding

This research are partially supported by National Natural Science Foundation of China No. 71802110 and 71801049, Natural Science Foundation of Jiangsu Province No. BK20170894, Humanity and Social Science Foundation of Ministry of Education of China No. 17YJC630043 and 17YJC630231.