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Discrete time shock models involving runs

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  • Eryilmaz, Serkan

Abstract

In this paper, three different discrete time shock models are studied. In the first model, the failure occurs when the additively accumulated damage exceeds a certain level while in the second model the system fails upon the local damage caused by the consecutively occurring shocks. The third model is a mixed model and combines the first and second models. The survival functions of the systems under these models are obtained when the occurrences of the shocks are independent, and when they are Markov dependent over the periods.

Suggested Citation

  • Eryilmaz, Serkan, 2015. "Discrete time shock models involving runs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 93-100.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:93-100
    DOI: 10.1016/j.spl.2015.08.007
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    References listed on IDEAS

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    1. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.
    2. Frosso Makri & Zaharias Psillakis, 2011. "On runs of length exceeding a threshold: normal approximation," Statistical Papers, Springer, vol. 52(3), pages 531-551, August.
    3. repec:cup:astinb:v:18:y:1988:i:02:p:161-168_00 is not listed on IDEAS
    4. Fermín Mallor & Javier Santos, 2003. "Reliability of systems subject to shocks with a stochastic dependence for the damages," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 427-444, December.
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    Cited by:

    1. Eryilmaz, Serkan, 2024. "Reliability and performance evaluation of weighted k-out-of-n:G system consisting of components with discrete lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    2. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
    3. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. Yanbo Song & Xiaoyue Wang, 2022. "Reliability Analysis of the Multi-State k -out-of- n : F Systems with Multiple Operation Mechanisms," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    5. Hamed Lorvand & Alireza Nematollahi, 2025. "On the reliability and the optimal replacement policy of a k-out-of-n system in a discrete shock model," Journal of Risk and Reliability, , vol. 239(5), pages 1061-1069, October.
    6. Stathis Chadjiconstantinidis, 2025. "A generalized censored $$\delta$$ δ -shock model for multi-state systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(4), pages 846-895, December.
    7. Anastasios N. Arapis & Frosso S. Makri & Zaharias M. Psillakis, 2017. "Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.

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