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Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems

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  • Yonit Barron
  • Uri Yechiali

Abstract

Consider a deteriorating repairable Markovian system with N stochastically independent identical units. The lifetime of each unit follows a discrete phase-type distribution. There is one online unit and the others are in standby status. In addition, there is a single repair facility and the repair time of a failed unit has a geometric distribution. The system is inspected at equally spaced points in time. After each inspection, either repair or a full replacement is possible. We consider state-dependent operating costs, repair costs that are dependent on the extent of the repair, and failure penalty costs. Applying dynamic programming, we show that under reasonable conditions on the system’s law of evolution and on the state-dependent costs, a generalized control-limit policy is optimal for the expected total discounted criterion for both cold standby and warm standby systems. Illustrative numerical examples are presented and insights are provided.

Suggested Citation

  • Yonit Barron & Uri Yechiali, 2017. "Generalized control-limit preventive repair policies for deteriorating cold and warm standby Markovian systems," IISE Transactions, Taylor & Francis Journals, vol. 49(11), pages 1031-1049, November.
    • Handle: RePEc:taf:uiiexx:v:49:y:2017:i:11:p:1031-1049
    DOI: 10.1080/24725854.2017.1335919
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    References listed on IDEAS

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    1. Yonit Barron, 2015. "Group replacement policies for a repairable cold standby system with fixed lead times," IISE Transactions, Taylor & Francis Journals, vol. 47(10), pages 1139-1151, October.
    2. Maliheh Aramon Bajestani & Dragan Banjevic, 2016. "Calendar-based age replacement policy with dependent renewal cycles," IISE Transactions, Taylor & Francis Journals, vol. 48(11), pages 1016-1026, November.
    3. Jianlan Zhong & Yizhong Ma & Y.L. Tu, 2016. "Integration of SPC and performance maintenance for supply chain system," International Journal of Production Research, Taylor & Francis Journals, vol. 54(19), pages 5932-5945, October.
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    Cited by:

    1. Liang, Zhenglin & Parlikad, Ajith Kumar, 2020. "Predictive group maintenance for multi-system multi-component networks," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    3. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    4. Evsey Morozov & Vladimir Rykov, 2023. "On the Positive Recurrence of Finite Regenerative Stochastic Models," Mathematics, MDPI, vol. 11(23), pages 1-11, November.
    5. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Joby K. Jose & M. Drisya, 2020. "Time-dependent stress–strength reliability models based on phase type distribution," Computational Statistics, Springer, vol. 35(3), pages 1345-1371, September.
    7. Ravi Suman & Ananth Krishnamurthy, 2020. "Analysis of tandem polling queues with finite buffers," Annals of Operations Research, Springer, vol. 293(1), pages 343-369, October.
    8. Wu, Hui & Li, Yan-Fu & Bérenguer, Christophe, 2020. "Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Nooshin Salari & Viliam Makis, 2020. "Joint maintenance and just-in-time spare parts provisioning policy for a multi-unit production system," Annals of Operations Research, Springer, vol. 287(1), pages 351-377, April.
    10. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.

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