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A shock and wear model with dependence between the interarrival failures

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  • Montoro-Cazorla, Delia
  • Pérez-Ocón, Rafael

Abstract

The Markovian arrival process is a suitable model for the arrival of external failures, it has the relevant property of dependence between the consecutive interarrival times. In the present paper we consider a shock and wear system in which the interarrival of the internal failures are also dependent, and a Markovian arrival process is used for modeling the arrival of this type of failures. So, we present a system under two types of failure governed by two independent Markovian arrival processes. The failures can be repairable or not. Two types of repair are considered: minimal and perfect, the first one is an instantaneous repair and the repair time of the second one is governed by a phase-type distribution. Under these conditions, two systems are considered, depending on the finite number of minimal repairs before a replacement would be random or fixed. For these systems, the stationary distribution, the number of minimal and perfect repairs, and the number of replacements are calculated. Some special cases of the systems are presented, showing the generality of the models. A numerical application illustrates the results.

Suggested Citation

  • Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2015. "A shock and wear model with dependence between the interarrival failures," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 339-352.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:339-352
    DOI: 10.1016/j.amc.2015.02.005
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    References listed on IDEAS

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    1. Frostig, Esther & Kenzin, Moshe, 2009. "Availability of inspected systems subject to shocks - A matrix algorithmic approach," European Journal of Operational Research, Elsevier, vol. 193(1), pages 168-183, February.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
    3. Korczak, Edward & Levitin, Gregory, 2007. "Survivability of systems under multiple factor impact," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 269-274.
    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.
    5. Kenzin, Moshe & Frostig, Esther, 2009. "M out of n inspected systems subject to shocks in random environment," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1322-1330.
    6. Søren Asmussen, 2000. "Matrix‐analytic Models and their Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 193-226, June.
    7. Tang, Ya-yong & Lam, Yeh, 2006. "A [delta]-shock maintenance model for a deteriorating system," European Journal of Operational Research, Elsevier, vol. 168(2), pages 541-556, January.
    8. 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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