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Adaptive CUSUM charts for monitoring linear drifts in Poisson rates

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  • He, Feng
  • Shu, Lianjie
  • Tsui, Kwok-Leung

Abstract

There has been relatively less attention paid to the monitoring of linear drifts in Poisson rates. Although the conventional CUSUM charts can be used for monitoring linear drifts in Poisson rates, they often rely on the assumption of a known parameter. To get rid of this assumption, this paper develops adaptive CUSUM (ACUSUM) charts for monitoring drifts in Poisson rates. The basic idea is to first estimate the current Poisson mean level and then to dynamically update the likelihood ratio in the CUSUM chart based on the estimated mean. Three different mean estimators based on the exponentially weighted moving average (EWMA) schemes are discussed. The comparison results are shown to favor the ACUSUM chart, especially at small drifts.

Suggested Citation

  • He, Feng & Shu, Lianjie & Tsui, Kwok-Leung, 2014. "Adaptive CUSUM charts for monitoring linear drifts in Poisson rates," International Journal of Production Economics, Elsevier, vol. 148(C), pages 14-20.
    • Handle: RePEc:eee:proeco:v:148:y:2014:i:c:p:14-20
    DOI: 10.1016/j.ijpe.2013.11.004
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    References listed on IDEAS

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    1. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
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    Cited by:

    1. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    2. Zhang, Min & Nie, Guohua & He, Zhen, 2014. "Performance of cumulative count of conforming chart of variable sampling intervals with estimated control limits," International Journal of Production Economics, Elsevier, vol. 150(C), pages 114-124.
    3. Sun, Edward W. & Chen, Yi-Ting & Yu, Min-Teh, 2015. "Generalized optimal wavelet decomposing algorithm for big financial data," International Journal of Production Economics, Elsevier, vol. 165(C), pages 194-214.

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