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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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    2. Wang, Jiantai & Longyan, Tan & Ma, Xiaobing & Gao, Kaiye & Jia, Heping & Yang, Li, 2023. "Prognosis-driven reliability analysis and replacement policy optimization for two-phase continuous degradation," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    3. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2017. "A study of postponed replacement in a delay time model," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 70-79.
    4. 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).
    5. Li Yang & Yu Zhao & Xiaobing Ma & Qingan Qiu, 2018. "An optimal inspection and replacement policy for a two-unit system," Journal of Risk and Reliability, , vol. 232(6), pages 766-776, December.
    6. Cavalcante, Cristiano A.V. & Lopes, Rodrigo S. & Scarf, Philip A., 2021. "Inspection and replacement policy with a fixed periodic schedule," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    7. de Jonge, Bram & Teunter, Ruud & Tinga, Tiedo, 2017. "The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 21-30.
    8. van Staden, Heletjé E. & Deprez, Laurens & Boute, Robert N., 2022. "A dynamic “predict, then optimize” preventive maintenance approach using operational intervention data," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1079-1096.
    9. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    10. 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.
    11. Scarf, P.A. & Cavalcante, C.A.V. & Lopes, R.S., 2019. "Delay-time modelling of a critical system subject to random inspections," European Journal of Operational Research, Elsevier, vol. 278(3), pages 772-782.
    12. Yang, Li & Ma, Xiaobing & Peng, Rui & Zhai, Qingqing & Zhao, Yu, 2017. "A preventive maintenance policy based on dependent two-stage deterioration and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 201-211.
    13. Alotaibi, Naif M. & Scarf, Philip & Cavalcante, Cristiano A.V. & Lopes, Rodrigo S. & de Oliveira e Silva, André Luiz & Rodrigues, Augusto J.S. & Alyami, Salem A., 2023. "Modified-opportunistic inspection and the case of remote, groundwater well-heads," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    14. Zhang, Zihan & Yang, Li, 2020. "Postponed maintenance scheduling integrating state variation and environmental impact," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    15. Akcay, Alp, 2022. "An alert-assisted inspection policy for a production process with imperfect condition signals," European Journal of Operational Research, Elsevier, vol. 298(2), pages 510-525.
    16. Wang, Jia & Han, Xu & Zhang, Yun-an & Bai, Guanghan, 2021. "Modeling the varying effects of shocks for a multi-stage degradation process," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    17. 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).
    18. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    19. Wang, Jiantai & Ma, Xiaobing & Yang, Li & Qiu, Qingan & Shang, Lijun & Wang, Jingjing, 2024. "A hybrid inspection-replacement policy for multi-stage degradation considering imperfect inspection with variable probabilities," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    20. Zhang, Fengxia & Shen, Jingyuan & Ma, Yizhong, 2020. "Optimal maintenance policy considering imperfect repairs and non-constant probabilities of inspection errors," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    21. Andersen, Jesper Fink & Andersen, Anders Reenberg & Kulahci, Murat & Nielsen, Bo Friis, 2022. "A numerical study of Markov decision process algorithms for multi-component replacement problems," European Journal of Operational Research, Elsevier, vol. 299(3), pages 898-909.

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