IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v261y2025ics0951832025002923.html

Optimal load adjustment policy for multi-state k-out-of-n balanced systems with self-healing mechanisms

Author

Listed:
  • Dong, Qinglai
  • Bai, Mengmeng
  • Yan, Zhaoyao
  • Wu, Bei

Abstract

Balanced systems are widely used in safety-critical fields such as military weaponry, aerospace, and advanced energy storage technologies. Reliability analysis and load level adjustment policies are crucial for ensuring stable operation. This paper develops a two-stage shock model influenced by component load levels, which effectively captures the degradation processes and self-healing mechanisms of components in shock environments. By integrating the finite Markov chain embedding method with the PH distribution, this paper analyzes the impact of shocks and load levels on system and component states, deriving expressions for key reliability indices such as system reliability and lifetime moments. Additionally, the paper examines the optimal timing for load adjustments and proposes a dynamic load adjustment policy based on system operating time, aimed at optimizing system reliability, extending operational lifetime, and minimizing average adjustment costs. The efficacy of this policy is demonstrated through a comprehensive numerical example using a lithium-ion battery cell system.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:reensy:v:261:y:2025:i:c:s0951832025002923
    DOI: 10.1016/j.ress.2025.111091
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832025002923
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ress.2025.111091?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. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Optimal loading of repairable system with perfect product storage," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    2. Zhao, Xian & Chai, Xiaofei & Cao, Shuai & Qiu, Qingan, 2023. "Dynamic loading and condition-based maintenance policies for multi-state systems with periodic inspection," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    3. Zhao, Xian & Li, Rong & Cao, Shuai & Qiu, Qingan, 2023. "Joint modeling of loading and mission abort policies for systems operating in dynamic environments," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. 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).
    5. Kong, Xuefeng & Yang, Jun, 2020. "Reliability analysis of composite insulators subject to multiple dependent competing failure processes with shock duration and shock damage self-recovery," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimal system loading and aborting in additive multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    7. Chai, Xiaofei & Kilic, Onur A. & Veldman, Jasper & Teunter, Ruud H. & Zhao, Xian, 2024. "Condition-based reallocation and maintenance for a 1-out-of-2 pairs balanced system," European Journal of Operational Research, Elsevier, vol. 318(2), pages 618-628.
    8. Zhao, Xian & Han, He & Jiao, Chunhui & Qiu, Qingan, 2024. "Reliability modeling of k-out-of-n: F balanced systems with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    9. Maxim Finkelstein & Ji Hwan Cha, 2013. "Stochastic Modeling for Reliability," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-5028-2, March.
    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. Li, Meiyan & Wu, Bei, 2024. "Optimal condition-based opportunistic maintenance policy for two-component systems considering common cause failure," Reliability Engineering and System Safety, Elsevier, vol. 250(C).
    12. Dingguo Hua & Elsayed A. Elsayed, 2018. "Reliability approximation of k-out-of-n pairs: G balanced systems with spatially distributed units," IISE Transactions, Taylor & Francis Journals, vol. 50(7), pages 616-626, July.
    13. Ranjkesh, Somayeh Hamed & Hamadani, Ali Zeinal & Mahmoodi, Safieh, 2019. "A new cumulative shock model with damage and inter-arrival time dependency," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    14. 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.
    15. Shriram S. Rangarajan & Suvetha Poyyamani Sunddararaj & AVV Sudhakar & Chandan Kumar Shiva & Umashankar Subramaniam & E. Randolph Collins & Tomonobu Senjyu, 2022. "Lithium-Ion Batteries—The Crux of Electric Vehicles with Opportunities and Challenges," Clean Technol., MDPI, vol. 4(4), pages 1-23, September.
    16. 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).
    17. Uit Het Broek, Michiel A.J. & Teunter, Ruud H. & de Jonge, Bram & Veldman, Jasper, 2021. "Joint condition-based maintenance and load-sharing optimization for two-unit systems with economic dependency," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1119-1131.
    18. Wu, Bei & Cui, Lirong & Fang, Chen, 2020. "Multi-state balanced systems with multiple failure criteria," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    19. Sheng-Jia Ruan & Yan-Hui Lin, 2021. "Reliability analysis and state transfer scheduling optimization of degrading load-sharing system equipped with warm standby components," Journal of Risk and Reliability, , vol. 235(6), pages 1166-1179, December.
    20. Qiu, Qingan & Cui, Lirong, 2019. "Optimal mission abort policy for systems subject to random shocks based on virtual age process," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 11-20.
    21. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Zhou, Jian, 2022. "Reliability analyses of k-out-of-n: F capability-balanced systems in a multi-source shock environment," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    22. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    23. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    24. 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).
    25. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    26. 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).
    27. Diouf, Boucar & Pode, Ramchandra, 2015. "Potential of lithium-ion batteries in renewable energy," Renewable Energy, Elsevier, vol. 76(C), pages 375-380.
    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. Mannai, Nizar & Jarray, Moujib, 2026. "Optimal design of k-out-of-n:G system under load redistribution and stochastic mission duration," Reliability Engineering and System Safety, Elsevier, vol. 269(C).
    2. 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).
    3. Baik, Seung Min & Cho, Yongkyu, 2026. "Lifetime analysis of circular k-out-of-n: G balanced systems in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).

    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. Dong, Bingchen & Liang, Zhenglin, 2026. "A novel method for reliability design of multi-tier circular (k,Smin)-out-of-(n1,…,nm,S): G balanced systems subject to external disturbances," Reliability Engineering and System Safety, Elsevier, vol. 266(PA).
    2. Baik, Seung Min & Cho, Yongkyu, 2026. "Lifetime analysis of circular k-out-of-n: G balanced systems in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 265(PB).
    3. 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).
    4. Zhao, Xian & Li, Ziyue & Wang, Xiaoyue & Qi, Xin, 2025. "Reliability and mission abort strategy for a multi-state k-out-of-n: F system in a dynamically changing shock environment," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    5. Fang, Chen & Chen, Jianhui & Qiu, Daizhen, 2024. "Reliability modeling for balanced systems considering mission abort policies," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    6. Xu, Dong & Tian, Yubin & Wang, Dianpeng & Shi, Junbiao, 2025. "Reliability analysis for a dynamic k-out-of-n system with thermal balance control," Reliability Engineering and System Safety, Elsevier, vol. 262(C).
    7. Qiu, Qingan & Liu, Bosen & Sun, Rongchi & Pei, Cuicui & Zhao, Xian, 2026. "Optimizing adaptive loading and abort decisions considering state-dependent reward," Reliability Engineering and System Safety, Elsevier, vol. 265(PA).
    8. Wu, Congshan & Zhao, Xian & Qiu, Qingan & Sun, Jinglei, 2021. "Optimal mission abort policy for k-out-of-n: F balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    9. 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).
    10. Xian Zhao & Rong Li & Yu Fan & Qingan Qiu, 2022. "Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism," Journal of Risk and Reliability, , vol. 236(1), pages 173-193, February.
    11. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Zhou, Jian, 2022. "Reliability analyses of k-out-of-n: F capability-balanced systems in a multi-source shock environment," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    12. 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).
    13. Zhao, Xian & He, Zongda & Wu, Yaguang & Qiu, Qingan, 2022. "Joint optimization of condition-based performance control and maintenance policies for mission-critical systems," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    14. Wang, Siqi & Li, Shuyun & Mo, Lipo, 2025. "Joint optimization of condition-based maintenance and component reallocation for phased-mission balanced systems with flexible structure considering imperfect substitution," Reliability Engineering and System Safety, Elsevier, vol. 264(PB).
    15. Gao, Hongda & Tu, Tengfei & Fang, Chen & Zhou, Xiaoguang, 2025. "Multi-state k-out-of-n: F network system performance evaluation by considering a balance dependence mechanism," Reliability Engineering and System Safety, Elsevier, vol. 264(PA).
    16. 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).
    17. Zhang, Yamei & Zhao, Songzheng & Wu, Bei, 2025. "Reliability and maintenance analysis of two-component system subject to zoned shocks and degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).
    18. 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).
    19. Zhao, Xian & Dong, Bingbing & Wang, Xiaoyue, 2023. "Reliability analysis of a two-dimensional voting system equipped with protective devices considering triggering failures," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    20. Yangyao, Shi & Xinchen, Zhuang & Tianxiang, Yu & Zijian, Zhang, 2023. "Multi-state balance system reliability research considering load influence," Reliability Engineering and System Safety, Elsevier, vol. 233(C).

    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:261:y:2025:i:c:s0951832025002923. 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.