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Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure

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  • Kim, Michael Jong
  • Jiang, Rui
  • Makis, Viliam
  • Lee, Chi-Guhn

Abstract

A new method for predicting failures of a partially observable system is presented. System deterioration is modeled as a hidden, 3-state continuous time homogeneous Markov process. States 0 and 1, which are not observable, represent good and warning conditions, respectively. Only the failure state 2 is assumed to be observable. The system is subject to condition monitoring at equidistant, discrete time epochs. The vector observation process is stochastically related to the system state. The objective is to develop a method for optimally predicting impending system failures. Model parameters are estimated using EM algorithm and a cost-optimal Bayesian fault prediction scheme is proposed. The method is illustrated using real data obtained from spectrometric analysis of oil samples collected at regular time epochs from transmission units of heavy hauler trucks used in mining industry. A comparison with other methods is given, which illustrates effectiveness of our approach.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:2:p:331-339
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    Cited by:

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    2. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    3. Jafari, L. & Makis, V., 2015. "Joint optimal lot sizing and preventive maintenance policy for a production facility subject to condition monitoring," International Journal of Production Economics, Elsevier, vol. 169(C), pages 156-168.
    4. Duan, Chaoqun & Li, Yifan & Pu, Huayan & Luo, Jun, 2022. "Adaptive monitoring scheme of stochastically failing systems under hidden degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    5. 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.
    6. Duan, Chaoqun & Makis, Viliam & Deng, Chao, 2020. "A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    7. Yuri S. Popkov & Yuri A. Dubnov & Alexey Yu. Popkov, 2016. "New Method of Randomized Forecasting Using Entropy-Robust Estimation: Application to the World Population Prediction," Mathematics, MDPI, vol. 4(1), pages 1-16, March.
    8. 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.
    9. Walter, Gero & Flapper, Simme Douwe, 2017. "Condition-based maintenance for complex systems based on current component status and Bayesian updating of component reliability," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 227-239.
    10. Yeong, Wai Chung & Khoo, Michael B.C. & Lee, Ming Ha & Rahim, M.A., 2013. "Economic and economic statistical designs of the synthetic X¯ chart using loss functions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 571-581.
    11. Shi, Yue & Zhu, Weihang & Xiang, Yisha & Feng, Qianmei, 2020. "Condition-based maintenance optimization for multi-component systems subject to a system reliability requirement," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    12. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    13. C. Drent & S. Kapodistria & J. A. C. Resing, 2019. "Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 269-308, December.
    14. Schücking, Maximilian & Jochem, Patrick, 2021. "Two-stage stochastic program optimizing the cost of electric vehicles in commercial fleets," Applied Energy, Elsevier, vol. 293(C).
    15. Jorgen-Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Annals of Operations Research, Springer, vol. 326(1), pages 295-316, July.
    16. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03634370, HAL.
    17. 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.
    18. Fernández, Arturo J., 2012. "Minimizing the area of a Pareto confidence region," European Journal of Operational Research, Elsevier, vol. 221(1), pages 205-212.
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    20. Hao Zhang & Weihua Zhang, 2023. "Analytical Solution to a Partially Observable Machine Maintenance Problem with Obvious Failures," Management Science, INFORMS, vol. 69(7), pages 3993-4015, July.

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