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Assessment of a multi-state system under a shock model

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  • Eryilmaz, Serkan

Abstract

A system is subject to random shocks over time. Let c1 and c2 be two critical levels such that c1 < c2. A shock with a magnitude between c1 and c2 has a partial damage on the system, and the system transits into a lower partially working state upon the occurrence of each shock in (c1, c2). A shock with a magnitude above c2 has a catastrophic affect on the system and it causes a complete failure. Such a shock model creates a multi-state system having random number of states. The lifetime, the time spent by the system in a perfect functioning state, and the total time spent by the system in partially working states are defined and their survival functions are derived when the interarrival times between successive shocks follow phase-type distribution.

Suggested Citation

  • Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:1-8
    DOI: 10.1016/j.amc.2015.06.129
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    References listed on IDEAS

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    1. Baggio, Michele & Perrings, Charles, 2015. "Modeling adaptation in multi-state resource systems," Ecological Economics, Elsevier, vol. 116(C), pages 378-386.
    2. 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.
    3. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    4. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
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    Cited by:

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    15. Xiaofei Chai & Boyu Chen & Xian Zhao, 2023. "Optimal Mission Abort Decisions for Multi-Component Systems Considering Multiple Abort Criteria," Mathematics, MDPI, vol. 11(24), pages 1-12, December.
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