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Joint Optimization of Sampling and Control of Partially Observable Failing Systems

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  • Michael Jong Kim

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada; and Department of Decision Sciences, NUS Business School, Singapore, Republic of Singapore)

  • Viliam Makis

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

Abstract

Stochastic control problems that arise in reliability and maintenance optimization typically assume that information used for decision-making is obtained according to a predetermined sampling schedule. In many real applications, however, there is a high sampling cost associated with collecting such data. It is therefore of equal importance to determine when information should be collected and to decide how this information should be utilized for maintenance decision-making. This type of joint optimization has been a long-standing problem in the operations research and maintenance optimization literature, and very few results regarding the structure of the optimal sampling and maintenance policy have been published. In this paper, we formulate and analyze the joint optimization of sampling and maintenance decision-making in the partially observable Markov decision process framework. We prove the optimality of a policy that is characterized by three critical thresholds, which have practical interpretation and give new insight into the value of condition-based maintenance programs in life-cycle asset management. Illustrative numerical comparisons are provided that show substantial cost savings over existing suboptimal policies.

Suggested Citation

  • Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:3:p:777-790
    DOI: 10.1287/opre.2013.1171
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    Cited by:

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    2. Xiao, Xiao & Jiang, Wei & Luo, Jianwen, 2019. "Combining process and product information for quality improvement," International Journal of Production Economics, Elsevier, vol. 207(C), pages 130-143.
    3. Lam, Ji Ye Janet & Banjevic, Dragan, 2015. "A myopic policy for optimal inspection scheduling for condition based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 1-11.
    4. Akram Khaleghei & Viliam Makis, 2015. "Model parameter estimation and residual life prediction for a partially observable failing system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 190-205, April.
    5. Duan, Chaoqun & Makis, Viliam & Deng, Chao, 2020. "A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    6. Azizi, Fariba & Salari, Nooshin, 2023. "A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    7. Jue Wang, 2016. "Minimizing the false alarm rate in systems with transient abnormality," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 320-334, June.
    8. Zhao, Yunfei & Smidts, Carol, 2022. "Reinforcement learning for adaptive maintenance policy optimization under imperfect knowledge of the system degradation model and partial observability of system states," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    9. Zheng, Rui & Xing, Yuan & Ren, Xiangyun, 2023. "Multilevel preventive replacement for a system subject to internal deterioration, external shocks, and dynamic missions," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    10. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    11. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    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. 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.
    14. 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).
    15. C. Drent & S. Kapodistria & J. A. C. Resing, 2019. "Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 269-308, December.
    16. Michael Jong Kim, 2020. "Variance Regularization in Sequential Bayesian Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 966-992, August.
    17. Ramin Moghaddass & Şeyda Ertekin, 2018. "Joint optimization of ordering and maintenance with condition monitoring data," Annals of Operations Research, Springer, vol. 263(1), pages 271-310, April.
    18. Chiel van Oosterom & Lisa M. Maillart & Jeffrey P. Kharoufeh, 2017. "Optimal maintenance policies for a safety‐critical system and its deteriorating sensor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 399-417, August.
    19. van Staden, Heletjé E. & Boute, Robert N., 2021. "The effect of multi-sensor data on condition-based maintenance policies," European Journal of Operational Research, Elsevier, vol. 290(2), pages 585-600.
    20. Liu, Xingchen & Sun, Qiuzhuang & Ye, Zhi-Sheng & Yildirim, Murat, 2021. "Optimal multi-type inspection policy for systems with imperfect online monitoring," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    21. Abderrahmane Abbou & Viliam Makis, 2019. "Group Maintenance: A Restless Bandits Approach," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 719-731, October.
    22. Chen, Nan & Ye, Zhi-Sheng & Xiang, Yisha & Zhang, Linmiao, 2015. "Condition-based maintenance using the inverse Gaussian degradation model," European Journal of Operational Research, Elsevier, vol. 243(1), pages 190-199.
    23. Michael Jong Kim, 2016. "Robust Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 64(4), pages 999-1014, August.

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