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Model parameter estimation and residual life prediction for a partially observable failing system

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  • Akram Khaleghei
  • Viliam Makis

Abstract

We consider a partially observable degrading system subject to condition monitoring and random failure. The system's condition is categorized into one of three states: a healthy state, a warning state, and a failure state. Only the failure state is observable. While the system is operational, vector data that is stochastically related to the system state is obtained through condition monitoring at regular sampling epochs. The state process evolution follows a hidden semi‐Markov model (HSMM) and Erlang distribution is used for modeling the system's sojourn time in each of its operational states. The Expectation‐maximization (EM) algorithm is applied to estimate the state and observation parameters of the HSMM. Explicit formulas for several important quantities for the system residual life estimation such as the conditional reliability function and the mean residual life are derived in terms of the posterior probability that the system is in the warning state. Numerical examples are presented to demonstrate the applicability of the estimation procedure and failure prediction method. A comparison results with hidden Markov modeling are provided to illustrate the effectiveness of the proposed model. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 190–205, 2015

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:3:p:190-205
    DOI: 10.1002/nav.21622
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    References listed on IDEAS

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    1. Michael Jong Kim & Viliam Makis & Rui Jiang, 2013. "Parameter estimation for partially observable systems subject to random failure," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(3), pages 279-294, May.
    2. Zhao, Xuejing & Fouladirad, Mitra & Bérenguer, Christophe & Bordes, Laurent, 2010. "Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 921-934.
    3. Carr, Matthew J. & Wang, Wenbin, 2011. "An approximate algorithm for prognostic modelling using condition monitoring information," European Journal of Operational Research, Elsevier, vol. 211(1), pages 90-96, May.
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    5. 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.
    6. 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.
    7. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    8. Makis, Viliam & Wu, Jianmou & Gao, Yan, 2006. "An application of DPCA to oil data for CBM modeling," European Journal of Operational Research, Elsevier, vol. 174(1), pages 112-123, October.
    9. Zhou, Zhi-Jie & Hu, Chang-Hua & Xu, Dong-Ling & Chen, Mao-Yin & Zhou, Dong-Hua, 2010. "A model for real-time failure prognosis based on hidden Markov model and belief rule base," European Journal of Operational Research, Elsevier, vol. 207(1), pages 269-283, November.
    10. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
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    Cited by:

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    2. Feng Lu & Jipeng Jiang & Jinquan Huang & Xiaojie Qiu, 2018. "An Iterative Reduced KPCA Hidden Markov Model for Gas Turbine Performance Fault Diagnosis," Energies, MDPI, vol. 11(7), pages 1-21, July.
    3. Zhang, Jinchun & Xv, Feiyu & Hou, Jinxiu, 2023. "Degradation recognition and residual life analysis of gasifier firebrick in service using Hidden Semi-Markov Model," Energy, Elsevier, vol. 264(C).
    4. Nooshin Salari & Viliam Makis, 2020. "Joint maintenance and just-in-time spare parts provisioning policy for a multi-unit production system," Annals of Operations Research, Springer, vol. 287(1), pages 351-377, April.

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