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A Markov Chain Model for Approximating the Run Length Distributions of Poisson EWMA Charts under Linear Drifts

Author

Listed:
  • Honghao Zhao

    (Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China)

  • Huajun Tang

    (Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China)

  • Chuan Pang

    (Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China)

  • Huimin Jiang

    (Department of Decision Sciences, School of Business, Macau University of Science and Technology, Macau 999078, China)

Abstract

In addition to monitoring the Poisson mean rate with step shifts, increasing attention has been given to monitoring Poisson processes subject to linear trends. The exponentially weighted moving average (EWMA) control chart has been widely implemented to monitor normal processes, but it lacks investigation for detecting the Poisson mean change under a linear trend. In this paper, we analyze the performance of the EWMA chart by extending the Markov chain model from monitoring Poisson processes under a step shift to a Poisson process with linear drift. The results demonstrate that the proposed method is able to provide accurate average run length approximation, compared with the Monte Carlo simulation. Optimal design tables and sensitivity analysis are presented to facilitate the use of the EWMA chart in practice.

Suggested Citation

  • Honghao Zhao & Huajun Tang & Chuan Pang & Huimin Jiang, 2022. "A Markov Chain Model for Approximating the Run Length Distributions of Poisson EWMA Charts under Linear Drifts," Mathematics, MDPI, vol. 10(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4786-:d:1005238
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    References listed on IDEAS

    as
    1. Lianjie Shu & Wei Jiang & Zhang Wu, 2012. "Exponentially weighted moving average control charts for monitoring increases in Poisson rate," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 711-723.
    2. Honghao Zhao & Lianjie Shu & Wei Jiang & Kwok-Leung Tsui, 2015. "An adaptive CUSUM chart for monitoring poisson rates with increasing population sizes," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 9(5), pages 692-715.
    3. Champ, Charles W. & Woodall, William H. & Mohsen, Hassan A., 1991. "A generalized quality control procedure," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 211-218, March.
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