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Maintenance optimization under non-constant probabilities of imperfect inspections

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  • Driessen, J.P.C.
  • Peng, H.
  • van Houtum, G.J.

Abstract

In this research, we study a single-component system that is characterized by three distinct deterioration states, cf. the Delay Time Model: normal, defective, and failed. The system is inspected periodically, and preventive system maintenance is done after a given number of inspections. The inspections are imperfect, and the probability of an inspection error changes over the system's operation time. Our objective is to minimize the average cost over an infinite time horizon. We present exact cost evaluations for a given maintenance policy, and we compare our model with non-constant probabilities to a model that considers constant probabilities of inspection errors. Our computational study illustrates that the model with constant probabilities may yield, on average, 19% higher costs than the model using non-constant probabilities of inspection errors. These values depend on the chosen parameter values, but still give an indication of how large the difference between both models can be. Finally, we also present an extension in which a reliability constraint (in terms of average failures per time unit) is added to our problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:165:y:2017:i:c:p:115-123
    DOI: 10.1016/j.ress.2017.03.020
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    References listed on IDEAS

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    1. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    2. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V. & Dwight, R.A., 2013. "Imperfect inspection and replacement of a system with a defective state: A cost and reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 80-87.
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    5. 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.
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    Citations

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    Cited by:

    1. 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).
    2. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zhong, 2019. "Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 89-98.
    3. Alberti, Alexandre R. & Cavalcante, Cristiano A.V. & Scarf, Philip & Silva, André L.O., 2018. "Modelling inspection and replacement quality for a protection system," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 145-153.
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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).
    6. Mancuso, A. & Compare, M. & Salo, A. & Zio, E., 2021. "Optimal Prognostics and Health Management-driven inspection and maintenance strategies for industrial systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    7. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    8. 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.
    9. Zhang, Fengxia & Liao, Haitao & Shen, Jingyuan & Ma, Yizhong, 2024. "Optimal maintenance over a finite time horizon for a system under imperfect inspection and dynamic working environment," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    10. 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.
    11. Ye, Zhenggeng & Cai, Zhiqiang & Zhou, Fuli & Zhao, Jiangbin & Zhang, Pan, 2019. "Reliability analysis for series manufacturing system with imperfect inspection considering the interaction between quality and degradation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 345-356.
    12. 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.
    13. 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).
    14. Seyedhosseini, Seyed Mohammad & Moakedi, Hamid & Shahanaghi, Kamran, 2018. "Imperfect inspection optimization for a two-component system subject to hidden and two-stage revealed failures over a finite time horizon," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 141-156.
    15. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    16. Azimpoor, Samareh & Taghipour, Sharareh, 2021. "Joint inspection and product quality optimization for a system with delayed failure," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    17. 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).
    18. 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).

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