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A redundant n-system under shocks and repairs following Markovian arrival processes

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

Abstract

A system with n components, one online and the rest in standby subject to repair is considered. The shocks causing the failure of the system follow a Markovian arrival process and the successive repair times are governed by another Markovian arrival process independent of the first one. In this way, the interarrival times between successive shocks are dependent and the same for the successive repair times. The Markov process governing the system is constructed and it is studied in a transient and stationary regime, calculating the availability, the reliability and the rate of occurrence of failures. We show how this system extends others previously published in the literature. A numerical application is performed.

Suggested Citation

  • Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A redundant n-system under shocks and repairs following Markovian arrival processes," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 69-75.
    • Handle: RePEc:eee:reensy:v:130:y:2014:i:c:p:69-75
    DOI: 10.1016/j.ress.2014.05.002
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    References listed on IDEAS

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    1. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "Matrix stochastic analysis of the maintainability of a machine under shocks," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 11-17.
    2. 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.
    3. 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.
    4. Wang, Chaonan & Xing, Liudong & Amari, Suprasad V., 2012. "A fast approximation method for reliability analysis of cold-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 119-126.
    5. 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.
    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. Yu, Haiyang & Yalaoui, Farouk & Châtelet, Ėric & Chu, Chengbin, 2007. "Optimal design of a maintainable cold-standby system," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 85-91.
    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:

    1. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2016. "A warmstandby system under shocks and repair governed by MAPs," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 331-338.
    2. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2015. "Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 126-133.
    3. Chen, Ying & Wang, Ze & Li, YingYi & Kang, Rui & Mosleh, Ali, 2018. "Reliability analysis of a cold-standby system considering the development stages and accumulations of failure mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 1-12.
    4. Rodríguez, Joanna & Lillo, Rosa E. & Ramírez-Cobo, Pepa, 2016. "Dependence patterns for modeling simultaneous events," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 19-30.
    5. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    6. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).

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