IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v269y2026ics0951832025011998.html

Joint optimization of protection adjustment and preventive maintenance policies for multi-state self-healing systems with protective devices in a shock environment

Author

Listed:
  • Wang, Xiaoyue
  • Wang, Linlin
  • Chen, Xi
  • Ning, Ru
  • Zhou, Jian

Abstract

Utilizing protective devices (PDs), applying self-healing materials and implementing maintenance are common measures to improve the system reliability, which all incur costs. The problem is how to jointly arrange these measures under the minimization of the total cost. However, no existing research investigated the joint optimization of maintenance and protection adjustment strategies for self-healing systems with PDs. To fill this gap, this paper builds a multi-state self-healing system with a PD subjected to shocks and explores its joint optimal policies of protection adjustment and preventive maintenance. A new self-healing mechanism is proposed for the system, where existing damage caused by prior shocks is randomly repaired once the self-healing is triggered. This self-healing behavior of the system occurs when it endures a predefined consecutive number of unharmful shocks. According to the periodic inspection of the system's state, maintenance actions are determined and the protective level of the device is adjusted. For the system in each state, Markov decision process and value iteration algorithm are applied to derive the optimal joint policy. Three heuristic policies are proposed to conduct the comparative analyses and demonstrate the superiority of the proposed policy. Finally, the applicability of the proposed model is verified through numerical examples.

Suggested Citation

  • Wang, Xiaoyue & Wang, Linlin & Chen, Xi & Ning, Ru & Zhou, Jian, 2026. "Joint optimization of protection adjustment and preventive maintenance policies for multi-state self-healing systems with protective devices in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 269(C).
    • Handle: RePEc:eee:reensy:v:269:y:2026:i:c:s0951832025011998
    DOI: 10.1016/j.ress.2025.112000
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832025011998
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2025.112000?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Shen, Jingyuan & Hu, Jiawen & Ma, Yizhong, 2020. "Two preventive replacement strategies for systems with protective auxiliary parts subject to degradation and economic dependence," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. 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).
    3. Tingting Huang & Yuepu Zhao & David W. Coit & Loon-Ching Tang, 2021. "Reliability assessment and lifetime prediction of degradation processes considering recoverable shock damages," IISE Transactions, Taylor & Francis Journals, vol. 53(5), pages 614-628, May.
    4. 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).
    5. Qiao, Peirui & Ma, Yizhong & Luo, Ming & Shen, Jingyuan & Zhou, Hanting, 2024. "Reliability modeling and warranty optimization for products with self-healing under a dynamic shock environment," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    6. Wang, Xiaoyue & Chen, Xi & Zhao, Xian & Ning, Ru, 2024. "Reliability analysis of self-healing systems equipped with multi-component protective devices operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    7. Zhao, Xian & Li, Ziyue & Wang, Xiaoyue & Guo, Bin, 2023. "Reliability of performance-based system containing multiple load-sharing subsystems with protective devices considering protection randomness," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    8. Fauriat, William & Zio, Enrico, 2020. "Optimization of an aperiodic sequential inspection and condition-based maintenance policy driven by value of information," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    10. Lamballais, T. & Merschformann, M. & Roy, D. & de Koster, M.B.M. & Azadeh, K. & Suhl, L., 2022. "Dynamic policies for resource reallocation in a robotic mobile fulfillment system with time-varying demand," European Journal of Operational Research, Elsevier, vol. 300(3), pages 937-952.
    11. Kang, Fengming & Cui, Lirong & Ye, Zhisheng & Zhou, Yu, 2024. "Reliability analysis for systems with self-healing mechanism in degradation-shock dependence processes with changing degradation rate," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    12. Zhao, Sangqi & Wei, Yian & Cheng, Yao & Li, Yang, 2025. "A state-specific joint size, maintenance, and inventory policy for a k-out-of-n load-sharing system subject to self-announcing failures," Reliability Engineering and System Safety, Elsevier, vol. 257(PB).
    13. Zhao, Sangqi & Wei, Yian & Li, Yang & Cheng, Yao, 2026. "A multi-agent reinforcement learning (MARL) framework for designing an optimal state-specific hybrid maintenance policy for a series k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    14. Wei, Yian & Cheng, Yao, 2025. "An optimal two-dimensional maintenance policy for self-service systems with multi-task demands and subject to competing sudden and deterioration-induced failures," Reliability Engineering and System Safety, Elsevier, vol. 255(C).
    15. Zheng, Rui & Shen, Jingyuan, 2025. "An optimal self-healing policy with discrete resources," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    16. Meango, Toualith Jean-Marc & Ouali, Mohamed-Salah, 2020. "Failure interaction model based on extreme shock and Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    17. Ning, Ru & Wang, Xiaoyue & Zhao, Xian & Li, Ziyue, 2024. "Joint optimization of preventive maintenance and triggering mechanism for k-out-of-n: F systems with protective devices based on periodic inspection," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    18. Eryilmaz, Serkan, 2026. "Protection or redundancy: Which is better and when in terms of mean time to failure and cost?," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).
    19. Che Sidik, Nor Azwadi & Witri Mohd Yazid, Muhammad Noor Afiq & Mamat, Rizalman, 2017. "Recent advancement of nanofluids in engine cooling system," Renewable and Sustainable Energy Reviews, Elsevier, vol. 75(C), pages 137-144.
    20. Ye, Kewei & Wang, Han & Ma, Xiaobing, 2023. "A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    21. Wei, Yian & Li, Anchi & Li, Yang & Cheng, Yao, 2026. "An optimal predictive inspection and maintenance policy for a multi-state system: A belief-based SMDP approach," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Xiaoyue & Wang, Jingxuan & Zhao, Xian & Wang, Siqi & Wang, Linlin, 2026. "Optimal reassignment policy for a balanced system with multi-state subsystems supported by protective devices in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 270(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Xiaoyue & Wang, Jingxuan & Zhao, Xian & Wang, Siqi & Wang, Linlin, 2026. "Optimal reassignment policy for a balanced system with multi-state subsystems supported by protective devices in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 270(C).
    2. Ning, Ru & Wang, Xiaoyue & Zhao, Xian & Li, Ziyue, 2024. "Joint optimization of preventive maintenance and triggering mechanism for k-out-of-n: F systems with protective devices based on periodic inspection," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    3. Dong, Qinglai & Miao, Huanhuan & Sun, Mingjuan & Jia, Xujie, 2026. "Mission abort strategies for balanced systems with a multi-mode protective device," Reliability Engineering and System Safety, Elsevier, vol. 267(PA).
    4. Zhao, Sangqi & Wei, Yian & Li, Yang & Cheng, Yao, 2026. "An optimal joint maintenance and mission abort policy for a system executing multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    5. Gan, Shuyuan & Li, Jinjian & Zheng, Rui & She, Daoming, 2026. "Reliability analysis and maintenance optimization for systems with degradation-mitigation and shock-resistance subsystems," Reliability Engineering and System Safety, Elsevier, vol. 269(C).
    6. Wang, Xiaoyue & Chen, Xi & Zhao, Xian & Ning, Ru, 2024. "Reliability analysis of self-healing systems equipped with multi-component protective devices operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    7. Tian, Tianzi & Xing, Liudong & Miao, Zhuqing & Wang, Ning & Yang, Jun, 2026. "Reliability analysis of performance-based balanced systems with reconfigurable mechanisms and warm standby," Reliability Engineering and System Safety, Elsevier, vol. 269(C).
    8. Lin, Huizhong & Zhu, Mengmeng, 2025. "Damage-resistant CPS reliability modeling considering coupled system resistance effects," Reliability Engineering and System Safety, Elsevier, vol. 256(C).
    9. Zhao, Sangqi & Wei, Yian & Li, Yang & Cheng, Yao, 2026. "A multi-agent reinforcement learning (MARL) framework for designing an optimal state-specific hybrid maintenance policy for a series k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    10. Gan, Shuyuan & Zhang, Xu & Coit, David W. & Wang, Xiaoyue, 2026. "Optimization of maintenance and spares inventory with dependence between the system and environment," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    11. Jiang, Shan & Jia, Xujie, 2024. "Reliability assessment under continuous fatigue degradation and shock based on Markov renewal process," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    12. Qiao, Peirui & Ma, Yizhong & Luo, Ming & Shen, Jingyuan & Zhou, Hanting, 2024. "Reliability modeling and warranty optimization for products with self-healing under a dynamic shock environment," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    13. Qin, Xiangyu & Che, Ada & Wu, Bei, 2024. "Modeling coupling impacts of self-healing mechanisms and dynamic environments on systems subject to dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    14. Lyu, Hao & Li, Zhihang & Qiao, Xuehang & Lu, Bing & Xie, Hualong & Pecht, Michael, 2025. "Reliability analysis for multi-component system considering failure propagation and dependent competing failure process," Reliability Engineering and System Safety, Elsevier, vol. 259(C).
    15. Liu, Yongchao & Zhao, Xiujie & Wang, Guanjun & Liu, Peng, 2026. "A reliability-based maintenance policy for multi-state systems subjecting to δ-shock," Reliability Engineering and System Safety, Elsevier, vol. 267(PA).
    16. Huang, Zhiyi & Wei, Yian & Cheng, Yao, 2025. "A quantitative framework for performance-based reliability prediction for a multi-component system subject to dynamic self-reconfiguration," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    17. Xiang, Shihu & Zhao, Changdong & Hao, Songhua & Li, Kui & Li, Wenhua, 2023. "A reliability evaluation method for electromagnetic relays based on a novel degradation-threshold-shock model with two-sided failure thresholds," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    18. Dong, Qinglai & Bai, Mengmeng & Yan, Zhaoyao & Wu, Bei, 2025. "Optimal load adjustment policy for multi-state k-out-of-n balanced systems with self-healing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 261(C).
    19. Zhao, Xian & Qi, Xin & Wang, Xiaoyue, 2023. "Reliability assessment for coherent systems operating under a generalized mixed shock model with multiple change points of the environment," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    20. Liu, Lujie & Yang, Jun & Zheng, Huiling & Li, Lei & Wang, Ning, 2025. "A dynamic multi-task selective execution policy considering stochastic dependence between degradation and random shocks by deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:269:y:2026:i:c:s0951832025011998. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.