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A warmstandby system under shocks and repair governed by MAPs

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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 source of failures of the online unit is different from the one of the standby units. They are governed by two independent Markovian arrival processes. The repair times also follow another Markovian arrival process, independent of the previous ones. As a consequence of these assumptions, the interarrival times between failures are dependent, and the same for the consecutive repair times. The multidimensional Markov process governing the system is constructed and the availability, reliability, and the rate of occurrence of failures are calculated. The renewal process associated to the replacements when the system is down is determined and the number of replacements with time are calculated. This system is general in several ways and it extends others previously published in the literature. A numerical application considering three simulated MAPs is performed; the descriptors of the MAPs and the performance measures of the system are calculated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:152:y:2016:i:c:p:331-338
    DOI: 10.1016/j.ress.2016.03.023
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Perez-Ocon, Rafael & Montoro-Cazorla, Delia, 2006. "A multiple warm standby system with operational and repair times following phase-type distributions," European Journal of Operational Research, Elsevier, vol. 169(1), pages 178-188, February.
    5. 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.
    6. 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. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    2. 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.
    3. 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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