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

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  • YuLong Qiao
  • JinSheng Sun
  • Philippe Castagliola
  • XueLong Hu

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.

Suggested Citation

  • YuLong Qiao & JinSheng Sun & Philippe Castagliola & XueLong Hu, 2022. "Optimal design of one-sided exponential EWMA charts based on median run length and expected median run length," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(9), pages 2887-2907, March.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:9:p:2887-2907
    DOI: 10.1080/03610926.2020.1782937
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    Cited by:

    1. Vasileios Alevizakos & Arpita Chatterjee & Kashinath Chatterjee & Christos Koukouvinos, 2024. "The exponentiated exponentially weighted moving average control chart," Statistical Papers, Springer, vol. 65(6), pages 3853-3891, August.
    2. Moi Hua Tuh & Cynthia Mui Lian Kon & Hong Siang Chua & Man Fai Lau & Yee Hui Robin Chang, 2023. "Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length," Mathematics, MDPI, vol. 11(3), pages 1-23, January.

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