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Lifetime properties of a cumulative shock model with a cluster structure

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  • Jian-Ming Bai
  • Zhe Zhang
  • Ze-Hui Li

Abstract

This paper studies a generalized cumulative shock model with a cluster shock structure. The system considered is subject to two types of shocks, called primary shocks and secondary shocks, where each primary shock causes a series of secondary shocks. The lifetime behavior of such a system becomes more complicated than that of a classical model with only one class of shocks. Under a non-homogeneous Poisson process of primary shocks, we analyze the lifetime behavior of the system with light-tailed and heavy-tailed distributed secondary shocks. We show some important characteristics of lifetime of this type of system. Our model, as an extension of the classical shock models, has wide applications in maintenance engineering, operations management, and insurance risk assessment. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Jian-Ming Bai & Zhe Zhang & Ze-Hui Li, 2014. "Lifetime properties of a cumulative shock model with a cluster structure," Annals of Operations Research, Springer, vol. 212(1), pages 21-41, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:21-41:10.1007/s10479-012-1255-6
    DOI: 10.1007/s10479-012-1255-6
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    References listed on IDEAS

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    1. Zehui Li & Xinbing Kong, 2007. "A new risk model based on policy entrance process and its weak convergence properties," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(3), pages 235-246, May.
    2. Shey-Huei Sheu & Chin-Chih Chang & Yu-Hung Chien, 2011. "Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks," Annals of Operations Research, Springer, vol. 186(1), pages 317-329, June.
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    Cited by:

    1. Parvardeh, A. & Balakrishnan, N., 2015. "On mixed δ-shock models," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 51-60.
    2. Mohsen Bohlooli-Zefreh & Afshin Parvardeh & Majid Asadi, 2023. "On the occurrence time of an extreme damage in a general shock model," Journal of Risk and Reliability, , vol. 237(6), pages 1100-1113, December.
    3. 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.
    4. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).

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