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An extended extreme shock maintenance model for a deteriorating system

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  • Chen, Jinyuan
  • Li, Zehui

Abstract

In this paper, we study a deteriorating system which is suffering random shocks from its environment. Assume that in the system's operating stage, whenever a shock arrives, it will do some damage to the system, but shocks with a “small†level of damage are harmless for the system, while shocks with a “large†level of damage may result in the system's failure. The system's deterioration is caused by both the external shocks and the internal load. In the external, the magnitude of the shock damage the system can bear is decreasing with respect to the number of repairs taken. In the internal, the consecutive repair time is increasing in the number of repairs taken. A replacement policy N, by which the system is replaced at the time of the Nth failure, is adopted. An explicit expression of the long run average cost per unit time is derived, and an optimal policy N* for minimizing the long run average cost per unit time is determined analytically. A numerical example is also given.

Suggested Citation

  • Chen, Jinyuan & Li, Zehui, 2008. "An extended extreme shock maintenance model for a deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1123-1129.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:8:p:1123-1129
    DOI: 10.1016/j.ress.2007.09.008
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    References listed on IDEAS

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    Cited by:

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    3. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    4. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    5. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    6. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    7. Xian Zhao & Rong Li & Yu Fan & Qingan Qiu, 2022. "Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism," Journal of Risk and Reliability, , vol. 236(1), pages 173-193, February.
    8. Li, Xiang-Yu & Huang, Hong-Zhong & Li, Yan-Feng & Xiong, Xiaoyan, 2021. "A Markov regenerative process model for phased mission systems under internal degradation and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Lina Bian & Bo Peng & Yong Ye, 2023. "Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model," Mathematics, MDPI, vol. 11(21), pages 1-19, November.
    10. Ji Cha & Maxim Finkelstein & Francois Marais, 2014. "Survival of systems with protection subject to two types of external attacks," Annals of Operations Research, Springer, vol. 212(1), pages 79-91, January.
    11. Zhang, Yuan Lin & Wang, Guan Jun, 2009. "A geometric process repair model for a repairable cold standby system with priority in use and repair," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1782-1787.
    12. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    13. Leung, Kit Nam Francis & Zhang, Yuan Lin & Lai, Kin Keung, 2011. "Analysis for a two-dissimilar-component cold standby repairable system with repair priority," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1542-1551.
    14. Yang, Li & Ma, Xiaobing & Peng, Rui & Zhai, Qingqing & Zhao, Yu, 2017. "A preventive maintenance policy based on dependent two-stage deterioration and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 201-211.
    15. Yu, Miaomiao & Tang, Yinghui & Liu, Liping & Cheng, Jiang, 2013. "A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 310-323.
    16. Zhao, Bing & Yue, Dequan & Liao, Haitao & Liu, Yuanhui & Zhang, Xiaohong, 2021. "Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs," Reliability Engineering and System Safety, Elsevier, vol. 208(C).

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