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On the occurrence time of an extreme damage in a general shock model

Author

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  • Mohsen Bohlooli-Zefreh
  • Afshin Parvardeh
  • Majid Asadi

Abstract

In the literature of system reliability and other fields related to the time to occurrence of an event, shock models play an important role. In this paper, we assume that a system is subject to shocks that occur according to a counting process describing the number of shocks that arrive during a specified time interval. As the magnitude of the damage imposed to the system by each shock is a crucial parameter to the system’s survival, we investigate some important random variables related to this parameter. A random variable of interest associated with this process is the first time, after a pre-specified time s , at which the amount of a shock damage to the system gets greater than the maximum of damages imposed to the system until time s . We obtain the reliability function of this random variable and investigate various properties of it and some other related random variables. In order to explore further the results, we examine two commonly used processes in the literature, that is, the non-homogeneous Poisson process and the Pólya process.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:237:y:2023:i:6:p:1100-1113
    DOI: 10.1177/1748006X221119549
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    References listed on IDEAS

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    1. Jianming Bai & Yun Chen & Chun Yuan & Xiaoling Yin, 2015. "Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, March.
    2. Eryilmaz, Serkan & Kan, Cihangir, 2019. "Reliability and optimal replacement policy for an extreme shock model with a change point," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    3. Serkan Eryilmaz & Konul Bayramoglu, 2014. "Life behavior of $$\delta $$ δ -shock models for uniformly distributed interarrival times," Statistical Papers, Springer, vol. 55(3), pages 841-852, August.
    4. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.
    5. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    6. 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.
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