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Condition-based maintenance policy for a two-component balanced system with a multimode protective device

Author

Listed:
  • Fang, Haojun
  • Zheng, Rui
  • Xia, Xiangde
  • Hu, Chiwei

Abstract

This paper presents a condition-based maintenance policy for a two-component balanced system equipped with a multimode protective device. The balanced components follow the same deterioration process characterized as a continuous-time Markov chain. The system fails if a component jumps into the failure state or the two components are unbalanced, incurring costly corrective replacement. The protective device has three modes (0, 1, and 2) to enhance reliability and maintain balance. One protective mode is selected at an inspection epoch, where preventive replacement is not performed, for the next inspection interval. If the protective device fails, it can be repaired at the next inspection epoch. The goal is to determine the optimal policy that minimizes the average maintenance cost rate. This optimization problem is formulated within a semi-Markov decision process framework and solved using a policy iteration algorithm. A matrix-based method is developed to calculate the system’s transition probabilities. A case study demonstrates the effectiveness of the proposed approach.

Suggested Citation

  • Fang, Haojun & Zheng, Rui & Xia, Xiangde & Hu, Chiwei, 2025. "Condition-based maintenance policy for a two-component balanced system with a multimode protective device," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
  • Handle: RePEc:eee:reensy:v:262:y:2025:i:c:s0951832025003965
    DOI: 10.1016/j.ress.2025.111195
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    References listed on IDEAS

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    1. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    2. Liu, Hengchang & Li, Bo & Yao, Fengming & Hu, Gexi & Xie, Lei, 2024. "Maintenance optimization of multi-unit balanced systems using deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    3. Endharta, Alfonsus Julanto & Yun, Won Young & Ko, Young Myoung, 2018. "Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 226-236.
    4. Zheng, Rui & Zhao, Xufeng & Hu, Chaoming & Ren, Xiangyun, 2023. "A repair-replacement policy for a system subject to missions of random types and random durations," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    5. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Wu, Congshan, 2023. "Reliability assessments for two types of balanced systems with multi-state protective devices," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    6. Gan, Shuyuan & Hu, Hengheng & Coit, David W., 2023. "Maintenance optimization considering the mutual dependence of the environment and system with decreasing effects of imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    7. Zheng, Rui & Najafi, Seyedvahid & Zhang, Yingzhi, 2022. "A recursive method for the health assessment of systems using the proportional hazards model," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    8. 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).
    9. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan, 2021. "Joint optimization of condition-based and age-based replacement policy and inventory policy for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    10. Tian, Tianzi & Yang, Jun & Li, Lei & Wang, Ning, 2023. "Reliability assessment of performance-based balanced systems with rebalancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    11. Zheng, Rui & Chen, Bingkun & Gu, Liudong, 2020. "Condition-based maintenance with dynamic thresholds for a system using the proportional hazards model," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    12. Wang, Jingjing & Miao, Yonghao, 2021. "Optimal preventive maintenance policy of the balanced system under the semi-Markov model," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    13. Zheng, Rui & Fang, Haojun & Song, Yanying, 2024. "A condition-based maintenance policy for a two-component balanced system with dependent degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    14. Wang, Jingjing & Zheng, Rui & Lin, Tianran, 2022. "Maintenance modeling for balanced systems subject to two competing failure modes," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    15. Gan, Shuyuan & Shen, Nan, 2023. "Maintenance Optimization for a Production System Subject to Shocks Considering a Buffer Inventory and Production Defects," Reliability Engineering and System Safety, Elsevier, vol. 238(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.
    17. Lirong Cui & Hongda Gao & Yuchang Mo, 2018. "Reliability for k-out-of-n:F balanced systems with m sectors," IISE Transactions, Taylor & Francis Journals, vol. 50(5), pages 381-393, May.
    18. Zheng, Rui & Wang, Jingjing & Zhang, Yingzhi, 2023. "A hybrid repair-replacement policy in the proportional hazards model," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1011-1021.
    19. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan & Lin, Cong, 2021. "Optimal condition-based preventive maintenance policy for balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    20. Wu, Congshan & Zhao, Xian & Wang, Xiaoyue & Wang, Siqi, 2021. "Reliability analysis of performance-based balanced systems with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    21. Wang, Siqi & Zhao, Xian & Wu, Congshan & Wang, Xiaoyue, 2023. "Joint optimization of multi-stage component reassignment and preventive maintenance for balanced systems considering imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    22. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
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