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Reliability estimation of a system subject to condition monitoring with two dependent failure modes

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  • Akram Khaleghei
  • Viliam Makis

Abstract

A new competing risk model is proposed to calculate the Conditional Mean Residual Life (CMRL) and Conditional Reliability Function (CRF) of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. The degradation process can be represented by a three-state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times that provides partial information about the system is working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follow Marshal–Olkin bivariate exponential distributions. The Expectation–Maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in the warning state. A comparison with a previously published model is provided to illustrate the effectiveness of the proposed model using real data.

Suggested Citation

  • Akram Khaleghei & Viliam Makis, 2016. "Reliability estimation of a system subject to condition monitoring with two dependent failure modes," IISE Transactions, Taylor & Francis Journals, vol. 48(11), pages 1058-1071, November.
    • Handle: RePEc:taf:uiiexx:v:48:y:2016:i:11:p:1058-1071
    DOI: 10.1080/0740817X.2016.1189632
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    Cited by:

    1. 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).
    2. Hu, Jiawen & Shen, Jingyuan & Shen, Lijuan, 2020. "Opportunistic maintenance for two-component series systems subject to dependent degradation and shock," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Zhao, Xian & He, Zongda & Wu, Yaguang & Qiu, Qingan, 2022. "Joint optimization of condition-based performance control and maintenance policies for mission-critical systems," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    4. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    5. Duan, Chaoqun & Gong, Ting & Yan, Liangwen & Li, Xinmin, 2024. "Bi-level corrected residual life-based maintenance for deteriorating systems under competing risks," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    6. 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.
    7. Ye, Zhenggeng & Cai, Zhiqiang & Zhou, Fuli & Zhao, Jiangbin & Zhang, Pan, 2019. "Reliability analysis for series manufacturing system with imperfect inspection considering the interaction between quality and degradation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 345-356.
    8. 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).
    9. Liu, Xingchen & Sun, Qiuzhuang & Ye, Zhi-Sheng & Yildirim, Murat, 2021. "Optimal multi-type inspection policy for systems with imperfect online monitoring," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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