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Multivariate control charts based on the James–Stein estimator

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  • Wang, Hsiuying
  • Huwang, Longcheen
  • Yu, Jeng Hung

Abstract

In this study, we focus on improving parameter estimation in Phase I study to construct more accurate Phase II control limits for monitoring multivariate quality characteristics. For a multivariate normal distribution with unknown mean vector, the usual mean estimator is known to be inadmissible under the squared error loss function when the dimension of the variables is greater than 2. Shrinkage estimators, such as the James–Stein estimators, are shown to have better performance than the conventional estimators in the literature. We utilize the James–Stein estimators to improve the Phase I parameter estimation. Multivariate control limits for the Phase II monitoring based on the improved estimators are proposed in this study. The resulting control charts, JS-type charts, are shown to have substantial performance improvement over the existing ones.

Suggested Citation

  • Wang, Hsiuying & Huwang, Longcheen & Yu, Jeng Hung, 2015. "Multivariate control charts based on the James–Stein estimator," European Journal of Operational Research, Elsevier, vol. 246(1), pages 119-127.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:1:p:119-127
    DOI: 10.1016/j.ejor.2015.02.046
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    References listed on IDEAS

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    1. Wang, Wenbin, 2012. "A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems," European Journal of Operational Research, Elsevier, vol. 218(3), pages 726-734.
    2. Chan, L. Y. & Lai, C. D. & Xie, M. & Goh, T. N., 2003. "A two-stage decision procedure for monitoring processes with low fraction nonconforming," European Journal of Operational Research, Elsevier, vol. 150(2), pages 420-436, October.
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    Cited by:

    1. Song, Zhi & Mukherjee, Amitava & Zhang, Jiujun, 2021. "Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment," European Journal of Operational Research, Elsevier, vol. 289(1), pages 177-196.
    2. Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    3. Leoni, Roberto Campos & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2015. "The effect of the autocorrelation on the performance of the T2 chart," European Journal of Operational Research, Elsevier, vol. 247(1), pages 155-165.

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