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Constructing a Markov process for modelling a reliability system under multiple failures and replacements

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

Abstract

We present a reliability system subject to shocks, internal failures, and inspections. Shocks cause damage or failure to several units simultaneously. The units undergo internal failures. After an inspection, the units that have failed are replaced by new and identical ones. The shocks are governed by a Poisson process, the internal failures and the inspection times are exponentially distributed. Under these assumptions a Markov process governing the system is constructed. The states of the system are formed by state-vectors associated to the units of the system. The instantaneous transitions among the states are constructed by using intermediate functions and indicators. A system with three components illustrating the procedure is studied and a numerical application is performed, comparing the performance measures of the k-out-of-3 systems for k = 1, 2, 3.

Suggested Citation

  • Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    • Handle: RePEc:eee:reensy:v:173:y:2018:i:c:p:34-47
    DOI: 10.1016/j.ress.2017.12.017
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    References listed on IDEAS

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    1. Cui, Lirong & Chen, Jianhui & Wu, Bei, 2017. "New interval availability indexes for Markov repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 12-17.
    2. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, January.
    3. 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.
    4. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
    5. Tina Song, Wheyming & Lin, Peisyuan, 2018. "System reliability of stochastic networks with multiple reworks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 258-268.
    6. Park, Jae-Hyun, 2017. "Time-dependent reliability of wireless networks with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 47-61.
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    Cited by:

    1. Liang, Qingzhu & Yang, Yinghao & Zhang, Hang & Peng, Changhong & Lu, Jianchao, 2022. "Analysis of simplification in Markov state-based models for reliability assessment of complex safety systems," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    2. Gandoman, Foad H. & Ahmadi, Abdollah & Bossche, Peter Van den & Van Mierlo, Joeri & Omar, Noshin & Nezhad, Ali Esmaeel & Mavalizadeh, Hani & Mayet, Clément, 2019. "Status and future perspectives of reliability assessment for electric vehicles," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 1-16.

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