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δ-shock model based on Polya process and its optimal replacement policy

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  • Eryilmaz, Serkan

Abstract

Shock models are of great interest in engineering reliability. Among the others, the δ-shock model has been widely studied in the literature. In this model, the system breaks down due to the arrivals of two successive shocks which are too close to each other. That is, the system fails when the time between two consecutive shocks falls below a fixed threshold δ. In the literature, the δ-shock model has been mostly studied by assuming that shocks arrive according to a renewal process so that the interarrival times between shocks are independent and identically distributed. In the current paper, we consider the case when the shock arrival process is described by a Polya process which has dependent interarrival times. In particular, we obtain survival function and mean lifetime of the system and study the optimal replacement policy for the δ-shock model based on Polya process.

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  • Eryilmaz, Serkan, 2017. "δ-shock model based on Polya process and its optimal replacement policy," European Journal of Operational Research, Elsevier, vol. 263(2), pages 690-697.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:690-697
    DOI: 10.1016/j.ejor.2017.05.049
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    Cited by:

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    6. Levitin, Gregory & Finkelstein, Maxim & Li, Yan-Feng, 2020. "Balancing mission success probability and risk of system loss by allocating redundancy in systems operating with a rescue option," Reliability Engineering and System Safety, Elsevier, vol. 195(C).

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