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Conditional design of the EWMA median chart with estimated parameters

Author

Listed:
  • XueLong Hu
  • Philippe Castagliola
  • XiaoJian Zhou
  • AnAn Tang

Abstract

The exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.

Suggested Citation

  • XueLong Hu & Philippe Castagliola & XiaoJian Zhou & AnAn Tang, 2019. "Conditional design of the EWMA median chart with estimated parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1871-1889, April.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:8:p:1871-1889
    DOI: 10.1080/03610926.2018.1440310
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    Cited by:

    1. Shahid Hussain & Sun Mei & Muhammad Riaz & Saddam Akber Abbasi, 2020. "On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    2. Johannssen, Arne & Chukhrova, Nataliya & Castagliola, Philippe, 2022. "The performance of the hypergeometric np chart with estimated parameter," European Journal of Operational Research, Elsevier, vol. 296(3), pages 873-899.

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