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The variable parameters T $$^{2}$$ 2 chart with run rules

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Listed:
  • Alireza Faraz
  • Giovanni Celano
  • Erwin Saniga
  • C. Heuchenne
  • S. Fichera

Abstract

The Hotelling’s $$\textit{T}^{2 }$$ T 2 control chart with variable parameters (VP $$T^{2})$$ T 2 ) has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean shifts. In this paper, we investigate the statistical performance of the VP $$T^{2}$$ T 2 control chart coupled with run rules. We consider two well-known run rules schemes. Statistical performance is evaluated by using a Markov chain modeling the random shock mechanism of the monitored process. The in-control time interval of the process is assumed to follow an exponential distribution. A genetic algorithm has been designed to select the optimal chart design parameters. We provide an extensive numerical analysis indicating that the VP $$T^{2}$$ T 2 control chart with run rules outperforms other charts for small sizes of the mean shift expressed through the Mahalanobis distance. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Alireza Faraz & Giovanni Celano & Erwin Saniga & C. Heuchenne & S. Fichera, 2014. "The variable parameters T $$^{2}$$ 2 chart with run rules," Statistical Papers, Springer, vol. 55(4), pages 933-950, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:933-950
    DOI: 10.1007/s00362-013-0537-7
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    References listed on IDEAS

    as
    1. Alireza Faraz & Ahmad Parsian, 2006. "Hotelling’s T 2 control chart with double warning lines," Statistical Papers, Springer, vol. 47(4), pages 569-593, October.
    2. Asghar Seif & Alireza Faraz & C�dric Heuchenne & Erwin Saniga & M. B. Moghadam, 2011. "A modified economic-statistical design of the T-super-2 control chart with variable sample sizes and control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2459-2469, January.
    3. Chen, Yan-Kwang & Hsieh, Kun-Lin, 2007. "Hotelling's T2 charts with variable sample size and control limit," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1251-1262, November.
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    Cited by:

    1. Kim Phuc Tran & Philippe Castagliola & Giovanni Celano, 2018. "Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts," Statistical Papers, Springer, vol. 59(1), pages 387-413, March.

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