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A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K

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

Abstract

A reliability system subject to shocks producing damage and failure is considered. The source of shocks producing failures is governed by a Markovian arrival process. All the shocks produce deterioration and some of them failures, which can be repairable or non-repairable. Repair times are governed by a phase-type distribution. The number of deteriorating shocks that the system can stand is fixed. After a fatal failure the system is replaced by another identical one. For this model the availability, the reliability, and the rate of occurrence of the different types of failures are calculated. It is shown that this model extends other previously published in the literature.

Suggested Citation

  • Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:3:p:636-642
    DOI: 10.1016/j.ejor.2014.01.021
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    References listed on IDEAS

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    1. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    2. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2012. "A shock and wear system under environmental conditions subject to internal failures, repair, and replacement," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 55-61.
    3. Montoro-Cazorla, Delia & Perez-Ocon, Rafael, 2006. "Replacement times and costs in a degrading system with several types of failure: The case of phase-type holding times," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1193-1209, December.
    4. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    5. 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.
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
    7. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, December.
    8. 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.
    9. 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.
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    Cited by:

    1. 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.
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    3. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    4. Du, Shijia & Zeng, Zhiguo & Cui, Lirong & Kang, Rui, 2017. "Reliability analysis of Markov history-dependent repairable systems with neglected failures," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 134-142.
    5. María Luz Gámiz & Delia Montoro-Cazorla & María del Carmen Segovia-García & Rafael Pérez-Ocón, 2022. "MoMA Algorithm: A Bottom-Up Modeling Procedure for a Modular System under Environmental Conditions," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    6. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    7. 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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