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Reliability evaluation of Markov renewal shock models with multiple failure mechanisms

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  • Wu, Bei
  • Cui, Lirong

Abstract

In this article, two Markov renewal shock models with multiple failure mechanisms are developed based on the extreme shock model and cumulative shock model respectively. The shock size and interarrival time dependency is studied by assuming the sizes and interarrival times of shocks are governed by an absorbing Markov chain with finite state space. Under the competing risk extreme shock model, the system fails when a single shock of a large size occurs or when it enters the absorbing state whichever occurs first. Under the competing risk cumulative shock model, the system fails when it transfers to the absorbing state, or when the accumulation of sizes of the previous shocks exceeds a prespecified critical level, whichever occurs first. The methods to calculate the reliability functions and other reliability indexes under the proposed two Markov renewal shock models are provided. A special case that the shock arrival process is independent of the current state of the system is considered. The limiting behavior of the mean time to failure of the system under two models is discussed. Finally, a study case of lithium-ion battery systems is conducted to illustrate the proposed models and obtained results.

Suggested Citation

  • Wu, Bei & Cui, Lirong, 2020. "Reliability evaluation of Markov renewal shock models with multiple failure mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:reensy:v:202:y:2020:i:c:s0951832020305524
    DOI: 10.1016/j.ress.2020.107051
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    Cited by:

    1. Ye, Kewei & Wang, Han & Ma, Xiaobing, 2023. "A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Jiang, Shan & Jia, Xujie, 2024. "Reliability assessment under continuous fatigue degradation and shock based on Markov renewal process," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    4. Oliveira, Ricardo P. & Achcar, Jorge A. & Mazucheli, Josmar & Bertoli, Wesley, 2021. "A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    5. Wang, Chaonan & Liu, Qiongyang & Xing, Liudong & Guan, Quanlong & Yang, Chunhui & Yu, Min, 2022. "Reliability analysis of smart home sensor systems subject to competing failures," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    6. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2023. "Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

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