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Reliability assessment of system under a generalized cumulative shock model

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  • Min Gong
  • Serkan Eryilmaz
  • Min Xie

Abstract

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

Suggested Citation

  • Min Gong & Serkan Eryilmaz & Min Xie, 2020. "Reliability assessment of system under a generalized cumulative shock model," Journal of Risk and Reliability, , vol. 234(1), pages 129-137, February.
    • Handle: RePEc:sae:risrel:v:234:y:2020:i:1:p:129-137
    DOI: 10.1177/1748006X19864831
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    References listed on IDEAS

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    1. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    2. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
    3. Eryilmaz, Serkan, 2015. "Dynamic assessment of multi-state systems using phase-type modeling," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 71-77.
    4. Yan-Hui Lin & Yan-Fu Li & Enrico Zio, 2016. "Reliability assessment of systems subject to dependent degradation processes and random shocks," IISE Transactions, Taylor & Francis Journals, vol. 48(11), pages 1072-1085, November.
    5. Zhou, Xiaojun & Wu, Changjie & Li, Yanting & Xi, Lifeng, 2016. "A preventive maintenance model for leased equipment subject to internal degradation and external shock damage," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 1-7.
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    Cited by:

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    10. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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