Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length

Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length ($\mathrm{A}RL$) as the criterion to be optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length ($\mathrm{M}RL$) provides a more meaningful interpretation than the $\mathrm{A}RL$. In this paper, the $\mathrm{M}RL$ is used as an alternative performance criterion, and the AEWMA $\overline{X}$ chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA $\overline{X}$ chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA $\overline{X}$ chart, in terms of the $\mathrm{M}RL$ performance. The construction of the $\mathrm{M}RL$-based AEWMA $\overline{X}$ chart is also illustrated using an example, and it is compared with competing charts.

Keywords:

• Adaptive EWMA chart
• median run length
• average run length

Acknowledgements

The authors express their sincere thanks to the editor and the reviewers for their helpful suggestions and comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Science Foundation of Jiangsu Province [grant number BK20170894]; China Scholarship Council (CN) [grant number 201706840050]; Humanity and Social Science Youth foundation of Ministry of Education of China [grant number 17YJC630043].