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Reliability assessment for multi-state systems with state transition dependency

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  • Liu, Yu
  • Liu, Qinzhen
  • Xie, Chaoyang
  • Wei, Fayuan

Abstract

As multi-state system reliability models are capable of characterizing the multi-state nature of engineered systems in deteriorating process, they have received considerable concerns in the past few decades. Most reported works on multi-state system reliability modeling are, however, based on the premise that transitions among states of a system/component are stochastically independent. Sometimes, a system may experience the same environmental/working conditions when deteriorating from a better state to worse ones, and thus, state transitions of a system/component could be stochastically dependent. In this paper, a new reliability model for multi-state systems/components with state transition dependency is put forth. The dependency among state transitions is implicitly characterized by copula functions which offer a great flexibility of linking arbitrary marginal distributions together to construct a multivariate distribution. The reliability function of a population of multi-state systems/components and the conditional reliability function of each individual multi-state system/component given a set of observations are derived. The likelihood functions for model parameter estimation are formulated for two cases, i.e., continuous and discontinuous inspection strategies, and model selection criteria are customized to identify the most preferable model among candidates. Two illustrative examples, together with comparative studies, are presented to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Liu, Yu & Liu, Qinzhen & Xie, Chaoyang & Wei, Fayuan, 2019. "Reliability assessment for multi-state systems with state transition dependency," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 276-288.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:276-288
    DOI: 10.1016/j.ress.2019.03.013
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    as
    1. Liu, Yu & Chen, Yiming & Jiang, Tao, 2018. "On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations," European Journal of Operational Research, Elsevier, vol. 268(1), pages 113-127.
    2. Moghaddass, Ramin & Zuo, Ming J., 2012. "A parameter estimation method for a condition-monitored device under multi-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 94-103.
    3. Li, Wei & Zuo, Ming J., 2008. "Reliability evaluation of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 160-167.
    4. Ward, Eric J., 2008. "A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools," Ecological Modelling, Elsevier, vol. 211(1), pages 1-10.
    5. Eryilmaz, Serkan, 2016. "A reliability model for a three-state degraded system having random degradation rates," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 59-63.
    6. Linkan Bian & Nagi Gebraeel & Jeffrey P. Kharoufeh, 2015. "Degradation modeling for real-time estimation of residual lifetimes in dynamic environments," IISE Transactions, Taylor & Francis Journals, vol. 47(5), pages 471-486, May.
    7. Liang, Zhenglin & Parlikad, Ajith Kumar & Srinivasan, Rengarajan & Rasmekomen, Nipat, 2017. "On fault propagation in deterioration of multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 162(C), pages 72-80.
    8. Li, Heping & Deloux, Estelle & Dieulle, Laurence, 2016. "A condition-based maintenance policy for multi-component systems with Lévy copulas dependence," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 44-55.
    9. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    10. Ramin Moghaddass & Ming J Zuo & Yu Liu & Hong-zhong Huang, 2015. "Predictive analytics using a nonhomogeneous semi-Markov model and inspection data," IISE Transactions, Taylor & Francis Journals, vol. 47(5), pages 505-520, May.
    11. Hong, Liu & Ouyang, Min & Peeta, Srinivas & He, Xiaozheng & Yan, Yongze, 2015. "Vulnerability assessment and mitigation for the Chinese railway system under floods," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 58-68.
    12. Xiang-Yu Li & Yu Liu & Chu-Jie Chen & Tao Jiang, 2016. "A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components," Journal of Risk and Reliability, , vol. 230(2), pages 133-146, April.
    13. Yan-Hui Lin & Yan-Fu Li & Enrico Zio, 2018. "Reliability Assessment of Systems with Dependent Degradation Processes Based on Piecewise-Deterministic Markov Process," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel & Alex Karagrigoriou (ed.), Recent Advances in Multi-state Systems Reliability, pages 213-225, Springer.
    14. Cui, Lirong & Li, Haijun, 2007. "Analytical method for reliability and MTTF assessment of coherent systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 300-307.
    15. Xing, Liudong & Levitin, Gregory, 2010. "Combinatorial analysis of systems with competing failures subject to failure isolation and propagation effects," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1210-1215.
    16. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, September.
    17. Philip A. Scarf & Mohammed Deara, 2003. "Block replacement policies for a two‐component system with failure dependence," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(1), pages 70-87, February.
    18. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    19. Min-Tsai Lai, 2007. "Periodical Replacement Model for a Multi-Unit System Subject to Failure Rate Interaction," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(3), pages 401-411, June.
    20. Wang, Wei & Maio, Francesco Di & Zio, Enrico, 2017. "Three-loop Monte Carlo simulation approach to Multi-State Physics Modeling for system reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 276-289.
    21. Levitin, Gregory & Xing, Liudong, 2010. "Reliability and performance of multi-state systems with propagated failures having selective effect," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 655-661.
    22. Koutras, V.P. & Malefaki, S. & Platis, A.N., 2017. "Optimization of the dependability and performance measures of a generic model for multi-state deteriorating systems under maintenance," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 73-86.
    23. Jiang, Tao & Liu, Yu, 2017. "Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 3-15.
    24. Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch & Dai, Yuanshun, 2011. "Multi-state systems with selective propagated failures and imperfect individual and group protections," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1657-1666.
    25. Wang, Chaonan & Xing, Liudong & Levitin, Gregory, 2012. "Propagated failure analysis for non-repairable systems considering both global and selective effects," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 96-104.
    26. Sun, Yong & Ma, Lin & Mathew, Joseph & Zhang, Sheng, 2006. "An analytical model for interactive failures," Reliability Engineering and System Safety, Elsevier, vol. 91(5), pages 495-504.
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