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Optimal repair–replacement policies for a system with two types of failures

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  • Wang, Guan Jun
  • Zhang, Yuan Lin

Abstract

In this paper, the optimal replacement problem is investigated for a system with two types of failures. One type of failure is repairable, which is conducted by a repairman when it occurs, and the other is unrepairable, which leads to a replacement of the system at once. The repair of the system is not “as good as new”. The consecutive operating times of the system after repair form a decreasing geometric process, while the repair times after failure are assumed to be independent and identically distributed. Replacement policy N is adopted, where N is the number of repairable failures. The system will be replaced at the Nth repairable failure or at the unrepairable failure, whichever occurs first. Two replacement models are considered, one is based on the limiting availability and the other based on the long-run average cost rate of the system. We give the explicit expressions for the limiting availability and the long-run average cost rate of the system under policy N, respectively. By maximizing the limiting availability A(N) and minimizing the long-run average cost rate C(N), we theoretically obtain the optimal replacement policies N∗ in both cases. Finally, some numerical simulations are presented to verify the theoretical results.

Suggested Citation

  • Wang, Guan Jun & Zhang, Yuan Lin, 2013. "Optimal repair–replacement policies for a system with two types of failures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 500-506.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:3:p:500-506
    DOI: 10.1016/j.ejor.2012.11.053
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    References listed on IDEAS

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    2. Safaei, Fatemeh & Ahmadi, Jafar & Balakrishnan, N., 2019. "A repair and replacement policy for repairable systems based on probability and mean of profits," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 143-152.
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    4. 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.
    5. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    6. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    7. Cha, Ji Hwan, 2016. "New stochastic models for preventive maintenance and maintenance optimizationAuthor-Name: Lee, Hyunju," European Journal of Operational Research, Elsevier, vol. 255(1), pages 80-90.
    8. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.
    9. Caiyun Niu & Jiang Jiang & Bingfeng Ge & Yingwu Chen, 2022. "Preventive maintenance model based on the renewal-geometric process," Journal of Risk and Reliability, , vol. 236(2), pages 348-356, April.

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