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A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems

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  • Wang, Wenbin

Abstract

When complex systems are monitored, multi-observations from several sensors or sources may be available. These observations can be fused through Bayesian theory to give a posterior probabilistic estimate of the underlying state which is often not directly observable. This forms the basis of a Bayesian control chart where the estimated posterior probability of the state can be compared with a preset threshold level to assess whether a full inspection is needed or not. Maintenance can then be carried out if indicated as necessary by the inspection. This paper considers the design of such multivariate Bayesian control chart where both the transition between states and the relationship between observed information and the state are not Markovian. Since analytical or numerical solutions are difficult for the case considered in this paper, Monte Carlo simulation is used to obtain the optimal control chart parameters, which are the monitoring interval and the upper control limit. A two-stage failure process characterised by the delay time concept is used to describe the underlying state transition process and Bayesian theory is used to compute the posterior probability of the underlying state, which is embedded in the simulation algorithm. Extensive examples are shown to demonstrate the modelling idea.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:726-734
    DOI: 10.1016/j.ejor.2011.12.010
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    References listed on IDEAS

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    1. Wenbin Wang, 2008. "Delay Time Modelling," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 14, pages 345-370, Springer.
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    14. Huda, Shamsul & Abdollahian, Mali & Mammadov, Musa & Yearwood, John & Ahmed, Shafiq & Sultan, Ibrahim, 2014. "A hybrid wrapper–filter approach to detect the source(s) of out-of-control signals in multivariate manufacturing process," European Journal of Operational Research, Elsevier, vol. 237(3), pages 857-870.
    15. Peng, Weiwen & Li, Yan-Feng & Mi, Jinhua & Yu, Le & Huang, Hong-Zhong, 2016. "Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 75-87.
    16. Wang, Wenbin, 2013. "Models of inspection, routine service, and replacement for a serviceable one-component system," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 57-63.
    17. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    18. Liu, Liping & Yu, Miaomiao & Ma, Yizhong & Tu, Yiliu, 2013. "Economic and economic-statistical designs of an X¯ control chart for two-unit series systems with condition-based maintenance," European Journal of Operational Research, Elsevier, vol. 226(3), pages 491-499.
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