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Optimal policies for a delay time model with postponed replacement

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  • van Oosterom, C.D.
  • Elwany, A.H.
  • Çelebi, D.
  • van Houtum, G.J.

Abstract

We develop a delay time model (DTM) to determine the optimal maintenance policy under a novel assumption: postponed replacement. Delay time is defined as the time lapse from the occurrence of a defect up until failure. Inspections can be performed to monitor the system state at non-negligible cost. Most works in the literature assume that instantaneous replacement is enforced as soon as a defect is detected at an inspection. In contrast, we relax this assumption and allow replacement to be postponed for an additional time period. The key motivation is to achieve better utilization of the system’s useful life, and reduce replacement costs by providing a sufficient time window to prepare maintenance resources. We model the preventive replacement cost as a non-increasing function of the postponement interval. We then derive the optimal policy under the modified assumption for a system with exponentially distributed defect arrival time, both for a deterministic delay time and for a more general random delay time. For the settings with a deterministic delay time, we also establish an upper bound on the cost savings that can be attained. A numerical case study is presented to benchmark the benefits of our modified assumption against conventional instantaneous replacement discussed in the literature.

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  • van Oosterom, C.D. & Elwany, A.H. & Çelebi, D. & van Houtum, G.J., 2014. "Optimal policies for a delay time model with postponed replacement," European Journal of Operational Research, Elsevier, vol. 232(1), pages 186-197.
  • Handle: RePEc:eee:ejores:v:232:y:2014:i:1:p:186-197
    DOI: 10.1016/j.ejor.2013.06.038
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    References listed on IDEAS

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    5. Zhang, Fengxia & Shen, Jingyuan & Liao, Haitao & Ma, Yizhong, 2021. "Optimal preventive maintenance policy for a system subject to two-phase imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
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    14. Driessen, J.P.C. & Peng, H. & van Houtum, G.J., 2017. "Maintenance optimization under non-constant probabilities of imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 115-123.
    15. Wang, Jingjing & Yang, Li & Ma, Xiaobing & Peng, Rui, 2021. "Joint optimization of multi-window maintenance and spare part provisioning policies for production systems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    16. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
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