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Optimal maintenance policy considering imperfect repairs and non-constant probabilities of inspection errors

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  • Zhang, Fengxia
  • Shen, Jingyuan
  • Ma, Yizhong

Abstract

During system operation, inspections are usually scheduled to detect the signals of defects. Due to the human, measurement or environment errors, inspections are generally imperfect which reveal the real states of the system with non-constant probabilities. When an inspection concludes a defect, necessary preventive maintenance actions should be carried out. In most existing literatures, perfect preventive maintenance, like replacement, is studied. However, in practice, most defects are imperfectly repaired rather than being replaced because of limitations of resources, technologies or time. Thus, considering both imperfect inspections and imperfect repairs, a novel preventive maintenance policy is investigated for a three-state system. Cost rate and reliability of the system are derived by a recursive method. The problem of optimal maintenance policy is formulated by minimizing the cost rate over an infinite time horizon. An algorithm is proposed to obtain the optimal inspection interval and preventive replacement interval. Finally, several numerical examples are given to illustrate the proposed method and verify the correctness of the method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:193:y:2020:i:c:s0951832019300274
    DOI: 10.1016/j.ress.2019.106615
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    as
    1. Wang, Huiying & Wang, Wenbin & Peng, Rui, 2017. "A two-phase inspection model for a single component system with three-stage degradation," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 31-40.
    2. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2018. "Conditional inspection and maintenance of a system with two interacting components," European Journal of Operational Research, Elsevier, vol. 268(2), pages 533-544.
    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.
    4. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    5. Zhao, Qian Qian & Yun, Won Young, 2019. "Storage availability of one-shot system under periodic inspection considering inspection error," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 120-133.
    6. 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.
    7. Flage, Roger, 2014. "A delay time model with imperfect and failure-inducing inspections," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 1-12.
    8. Park, Minjae & Jung, Ki Mun & Park, Dong Ho, 2018. "Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 1-9.
    9. 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.
    10. Zhao, Xian & Guo, Xiaoxin & Wang, Xiaoyue, 2018. "Reliability and maintenance policies for a two-stage shock model with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 185-194.
    11. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    12. MERCIER, Sophie & CASTRO, I.T., 2019. "Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system," European Journal of Operational Research, Elsevier, vol. 273(1), pages 237-248.
    13. Zhao, Jianmin & Chan, A.H.C. & Roberts, C. & Madelin, K.B., 2007. "Reliability evaluation and optimisation of imperfect inspections for a component with multi-defects," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 65-73.
    14. Xiujie Zhao & Olivier Gaudoin & Laurent Doyen & Min Xie, 2019. "Optimal inspection and replacement policy based on experimental degradation data with covariates," IISE Transactions, Taylor & Francis Journals, vol. 51(3), pages 322-336, March.
    15. 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.
    16. 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.
    17. 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.
    18. Aven, Terje & Castro, I.T., 2009. "A delay-time model with safety constraint," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 261-267.
    19. Wang, Wenbin & Zhao, Fei & Peng, Rui, 2014. "A preventive maintenance model with a two-level inspection policy based on a three-stage failure process," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 207-220.
    20. Le, Minh Duc & Tan, Cher Ming, 2013. "Optimal maintenance strategy of deteriorating system under imperfect maintenance and inspection using mixed inspectionscheduling," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 21-29.
    21. Liao, Gwo-Liang & Chen, Yen Hung & Sheu, Shey-Huei, 2009. "Optimal economic production quantity policy for imperfect process with imperfect repair and maintenance," European Journal of Operational Research, Elsevier, vol. 195(2), pages 348-357, June.
    22. Nafisah, Ibrahim & Shrahili, Mansour & Alotaibi, Naif & Scarf, Phil, 2019. "Virtual series-system models of imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 604-613.
    23. Grosse, E. H. & Glock, C. H. & Jaber, M. Y. & Neumann, W. P., 2015. "Incorporating human factors in order picking planning models: framework and research opportunities," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 65237, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    24. Lin, Boliang & Wu, Jianping & Lin, Ruixi & Wang, Jiaxi & Wang, Hui & Zhang, Xuhui, 2019. "Optimization of high-level preventive maintenance scheduling for high-speed trains," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 261-275.
    25. Eric H. Grosse & Christoph H. Glock & Mohamad Y. Jaber & W. Patrick Neumann, 2015. "Incorporating human factors in order picking planning models: framework and research opportunities," International Journal of Production Research, Taylor & Francis Journals, vol. 53(3), pages 695-717, February.
    26. Grosse, E. H., 2015. "Human factors in order picking systems – A framework for integrating human factors in order picking planning models with an in-depth analysis of learning effects," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 74359, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    27. Fei Zhao & Wenbin Wang & Rui Peng, 2015. "Delay-time-based preventive maintenance modelling for a production plant: a case study in a steel mill," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(12), pages 2015-2024, December.
    28. Kallen, M.J., 2011. "Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 636-641.
    29. Do, Phuc & Assaf, Roy & Scarf, Phil & Iung, Benoit, 2019. "Modelling and application of condition-based maintenance for a two-component system with stochastic and economic dependencies," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 86-97.
    30. 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.
    31. Liao, Haitao & Elsayed, Elsayed A. & Chan, Ling-Yau, 2006. "Maintenance of continuously monitored degrading systems," European Journal of Operational Research, Elsevier, vol. 175(2), pages 821-835, December.
    32. 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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    8. 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.
    9. Zhang, Lin & Chen, Xiaohui & Khatab, Abdelhakim & An, Youjun, 2022. "Optimizing imperfect preventive maintenance in multi-component repairable systems under s-dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
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    15. Bimal Kumar Sett & Bikash Koli Dey & Biswajit Sarkar, 2020. "Autonomated Inspection Policy for Smart Factory—An Improved Approach," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    16. 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).
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    18. Alberti, A.R. & Neto, W.A. Ferreira & Cavalcante, C.A.V. & Santos, A.C.J., 2022. "Modelling a flexible two-phase inspection-maintenance policy for safety-critical systems considering revised and non-revised inspections," Reliability Engineering and System Safety, Elsevier, vol. 221(C).

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