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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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    1. Castro, I.T. & Pérez-Ocón, R., 2006. "Reward optimization of a repairable system," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 311-319.
    2. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2006. "A deteriorating two-system with two repair modes and sojourn times phase-type distributed," Reliability Engineering and System Safety, Elsevier, vol. 91(1), pages 1-9.
    3. Lam Yeh & So Kuen Chan, 1998. "Statistical inference for geometric processes with lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 99-112, March.
    4. Kahle, Waltraud, 2007. "Optimal maintenance policies in incomplete repair models," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 563-565.
    5. Sheu, Shey-Huei & Lin, Yuh-Bin & Liao, Gwo-Liang, 2006. "Optimum policies for a system with general imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 362-369.
    6. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
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    Cited by:

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