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Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length

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  • H.W. You
  • Michael B.C. Khoo
  • P. Castagliola
  • Liang Qu

Abstract

This paper examines the exponentially weighted moving average (EWMA) chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance. Therefore, in this paper, the median run length (MRL) and expected MRL (EMRL) are used as alternative performance criteria. Additionally, the methodology for computing the EMRL of the EWMA chart with known process parameters is presented. Since the performance of the EWMA chart is affected by estimation error, a study on the minimum number of Phase-I samples required so that the chart with estimated parameters has a desired performance is conducted. As this study reveals that a large number of Phase-I samples are needed, optimal design procedures for minimising the out-of-control MRL and EMRL of the EWMA chart with estimated process parameters are suggested. By using these proposed procedures, the EWMA chart with estimated parameters will have a closer performance to its known parameters counterpart, even with a reasonable number of Phase-I samples. The construction of the MRL based EWMA chart with estimated parameters is illustrated using real data and compared with the corresponding chart based on ARL.

Suggested Citation

  • H.W. You & Michael B.C. Khoo & P. Castagliola & Liang Qu, 2016. "Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5073-5094, September.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:17:p:5073-5094
    DOI: 10.1080/00207543.2016.1145820
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    References listed on IDEAS

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    1. Khoo, Michael B.C. & Teoh, W.L. & Castagliola, Philippe & Lee, M.H., 2013. "Optimal designs of the double sampling X¯ chart with estimated parameters," International Journal of Production Economics, Elsevier, vol. 144(1), pages 345-357.
    2. Shichang Du & Xufeng Yao & Delin Huang, 2015. "Engineering model-based Bayesian monitoring of ramp-up phase of multistage manufacturing process," International Journal of Production Research, Taylor & Francis Journals, vol. 53(15), pages 4594-4613, August.
    3. Ying Zhang & Philippe Castagliola & Zhang Wu & Michael Khoo, 2011. "The synthetic [Xbar] chart with estimated parameters," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 676-687.
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    Cited by:

    1. 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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