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A hybrid repair-replacement policy in the proportional hazards model

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  • Zheng, Rui
  • Wang, Jingjing
  • Zhang, Yingzhi

Abstract

Cox's proportional hazards model is widely used to describe the hazard rate of a system deteriorating with age and diagnostic covariates. Existing maintenance in the proportional hazards model was primarily concerned with replacement, resulting in excessive maintenance for many repairable systems. This paper develops a novel hybrid repair-replacement model in the proportional hazards model with a stochastically increasing Markovian covariate process. Preventive repair reduces both age and covariate, and the reduction rate decreases as the number of repairs increases. At an inspection epoch where the system age, covariate state, and repair number are available, the decision-maker considers three possible actions, i.e., no maintenance, preventive repair, and preventive replacement. The objective is to derive the optimal policy that minimizes the long-run average maintenance cost rate. The optimization problem is formulated in the semi-Markov decision process (SMDP) framework. The structural properties of the optimal policy are examined to reduce the policy space. Then a policy-iteration algorithm with a backward policy-improvement step is developed for efficiently finding the optimization results. A practical numerical example with sensitivity analysis is conducted to illustrate the effectiveness of the proposed approach. A comparison with two heuristic policies confirms the superiority of the proposed policy in reducing maintenance costs.

Suggested Citation

  • Zheng, Rui & Wang, Jingjing & Zhang, Yingzhi, 2023. "A hybrid repair-replacement policy in the proportional hazards model," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1011-1021.
  • Handle: RePEc:eee:ejores:v:304:y:2023:i:3:p:1011-1021
    DOI: 10.1016/j.ejor.2022.05.020
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    References listed on IDEAS

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    4. Moezza Nabeel & Sajid Ali & Ismail Shah & Mohammed M. A. Almazah & Fuad S. Al-Duais, 2023. "Robust Surveillance Schemes Based on Proportional Hazard Model for Monitoring Reliability Data," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    5. Wang, Jiantai & Zhou, Shihan & Peng, Rui & Qiu, Qingan & Yang, Li, 2023. "An inspection-based replacement planning in consideration of state-driven imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

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