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On ARL-unbiased c-charts for INAR(1) Poisson counts

Author

Listed:
  • Sofia Paulino

    (Universidade de Lisboa)

  • Manuel Cabral Morais

    (University de Lisboa)

  • Sven Knoth

    (Helmut Schmidt University)

Abstract

Counts of nonconformities are frequently assumed to have a Poisson distribution. The integer and asymmetrical character of this distribution and the value of its target mean may prevent the quality control operator to deal with a chart with a pre-specified in-control average run length (ARL) and the ability to promptly detect both increases and decreases in the mean of those counts. Moreover, as far as we know, the c-chart proposed to monitor the mean of first-order integer-valued autoregressive [INAR(1)] Poisson counts tends to be ARL-biased, in the sense that it takes longer, in average, to detect some shifts in the process mean than to trigger a false alarm. In this paper, we capitalize on the randomization of the emission of a signal and on a nested secant rule search procedure not only to eliminate the bias of the ARL function of the c-chart for the mean of INAR(1) Poisson counts, but also to bring its in-control ARL exactly to a pre-specified and desired value. Striking illustrations of the resulting ARL-unbiased c-chart are provided.

Suggested Citation

  • Sofia Paulino & Manuel Cabral Morais & Sven Knoth, 2019. "On ARL-unbiased c-charts for INAR(1) Poisson counts," Statistical Papers, Springer, vol. 60(4), pages 1021-1038, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0861-9
    DOI: 10.1007/s00362-016-0861-9
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    References listed on IDEAS

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    1. Christian Weiß & Murat Testik, 2011. "The Poisson INAR(1) CUSUM chart under overdispersion and estimation error," IISE Transactions, Taylor & Francis Journals, vol. 43(11), pages 805-818.
    2. Huwang, Longcheen & Huang, Chun-Jung & Wang, Yi-Hua Tina, 2010. "New EWMA control charts for monitoring process dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2328-2342, October.
    3. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    4. M. F. Ramalhoto & M. Morais, 1999. "Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 129-160.
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