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Multivariate Bayesian Control Chart

Author

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  • Viliam Makis

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G8)

Abstract

A multivariate Bayesian control chart for monitoring process mean under the assumption that the vector of process observations follows a multivariate normal distribution is considered. Traditional control charts such as Hotelling's T 2 , EWMA, and CUSUM charts have been applied to control industrial processes characterized by several measurable variables. It is well known that these traditional, non-Bayesian process control techniques are not optimal, but very few results regarding the structure of the Bayesian control policy have been reported in the literature, all dealing with the univariate, finite-horizon case. In this paper, we formulate the multivariate Bayesian process control problem in the optimal stopping framework. The objective is to find a stopping rule under partial observations, minimizing the long-run expected average cost per unit time for a given sample size and sampling interval. Under standard operating and cost assumptions, it is proved that a control limit policy is optimal, and an algorithm is presented to find the optimal control limit and the minimum average cost.

Suggested Citation

  • Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:2:p:487-496
    DOI: 10.1287/opre.1070.0495
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    References listed on IDEAS

    as
    1. Joel M. Calabrese, 1995. "Bayesian Process Control for Attributes," Management Science, INFORMS, vol. 41(4), pages 637-645, April.
    2. V. Makis & X. Jiang, 2003. "Optimal Replacement Under Partial Observations," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 382-394, May.
    3. W. K. Chiu, 1976. "Economic Design of np Charts for Processes Subject to a Multiplicity of Assignable Causes," Management Science, INFORMS, vol. 23(4), pages 404-411, December.
    4. Tagaras, George, 1996. "Dynamic control charts for finite production runs," European Journal of Operational Research, Elsevier, vol. 91(1), pages 38-55, May.
    5. Evan L. Porteus & Alexandar Angelus, 1997. "Opportunities for Improved Statistical Process Control," Management Science, INFORMS, vol. 43(9), pages 1214-1228, September.
    6. James E. Eckles, 1968. "Optimum Maintenance with Incomplete Information," Operations Research, INFORMS, vol. 16(5), pages 1058-1067, October.
    7. Sheldon M. Ross, 1971. "Quality Control under Markovian Deterioration," Management Science, INFORMS, vol. 17(9), pages 587-596, May.
    8. Chelsea C. White, 1977. "A Markov Quality Control Process Subject to Partial Observation," Management Science, INFORMS, vol. 23(8), pages 843-852, April.
    9. George Tagaras & Yiannis Nikolaidis, 2002. "Comparing the Effectiveness of Various Bayesian X̄ Control Charts," Operations Research, INFORMS, vol. 50(5), pages 878-888, October.
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    Citations

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    Cited by:

    1. Tagaras, George, 2017. "New indices for the evaluation of the statistical properties of Bayesian x¯ control charts for short runsAuthor-Name: Nikolaidis, Yiannis," European Journal of Operational Research, Elsevier, vol. 259(1), pages 280-292.
    2. Kim, Michael Jong & Jiang, Rui & Makis, Viliam & Lee, Chi-Guhn, 2011. "Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure," European Journal of Operational Research, Elsevier, vol. 214(2), pages 331-339, October.
    3. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    4. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Remarks on Bayesian Control Charts," Papers 1712.02860, arXiv.org, revised Dec 2017.
    5. 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.
    6. Michael Jong Kim, 2016. "Robust Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 64(4), pages 999-1014, August.
    7. Zhang, Nan & Deng, Yingjun & Liu, Bin & Zhang, Jun, 2023. "Condition-based maintenance for a multi-component system in a dynamic operating environment," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    8. Sangahn Kim & Mehmet Turkoz, 2022. "Bayesian sequential update for monitoring and control of high-dimensional processes," Annals of Operations Research, Springer, vol. 317(2), pages 693-715, October.
    9. Akram Khaleghei & Viliam Makis, 2015. "Model parameter estimation and residual life prediction for a partially observable failing system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 190-205, April.
    10. Tang, Diyin & Makis, Viliam & Jafari, Leila & Yu, Jinsong, 2015. "Optimal maintenance policy and residual life estimation for a slowly degrading system subject to condition monitoring," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 198-207.
    11. Rui Jiang & Michael Kim & Viliam Makis, 2012. "A Bayesian model and numerical algorithm for CBM availability maximization," Annals of Operations Research, Springer, vol. 196(1), pages 333-348, July.
    12. Sait Tunç & Oguzhan Alagoz & Elizabeth S. Burnside, 2022. "A new perspective on breast cancer diagnostic guidelines to reduce overdiagnosis," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2361-2378, May.
    13. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    14. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.
    15. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

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