IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v208y2023icp637-659.html
   My bibliography  Save this article

Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates

Author

Listed:
  • Gao, Shan

Abstract

This paper considers the reliability analysis and the bi-objective optimal problem for a redundant system with two dependent failures: common cause failure (CCF) and load-sharing failure, where the system contains N active components, W warm standbys and C cold standbys, a K-mixed redundancy strategy is considered. In the system, there is a repair team providing variable repair rates according to differential situations: when there are standby components available in the system, the repair team assigns a regular repairman to repair the failed components, with the known fact that regular repairman is not as skilled as an expert repairman in doing some complex repair; when all the spares are exhausted, the repair team assigns an expert repairman to attend failed components; when the system breaks down due to a CCF’s occurrence, the repair team provides a very special repair service to restore the system to normal working state. The steady-state distribution of the system is obtained by matrix-analytic method. The sets of equations satisfied by the reliability functions and transient availabilities from arbitrary initial state are respectively presented and solved by Markov renewal theory, Laplace–Stieltjes transform (LST) and Laplace transform (LT) technique. Based on the obtained results, sensitivity analysis is performed by some numerical experiments. From economic view point, the bi-objective optimization problem is constructed and solved by NSGA-II algorithm for the minimal expected total cost and maximal availability.

Suggested Citation

  • Gao, Shan, 2023. "Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 637-659.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:637-659
    DOI: 10.1016/j.matcom.2023.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423000605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.02.001?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Yan-Feng Li & Hong-Zhong Huang & Jinhua Mi & Weiwen Peng & Xiaomeng Han, 2022. "Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability," Annals of Operations Research, Springer, vol. 311(1), pages 195-209, April.
    2. Shekhar, Chandra & Kumar, Amit & Varshney, Shreekant, 2020. "Load sharing redundant repairable systems with switching and reboot delay," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Cheng, Chen & Yang, Jun & Li, Lei, 2021. "Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state phased mission system with common bus performance sharing subjected to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Guo, Yongjin & Zhong, Mingjun & Gao, Chao & Wang, Hongdong & Liang, Xiaofeng & Yi, Hong, 2021. "A discrete-time Bayesian network approach for reliability analysis of dynamic systems with common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    6. Yu, Haiyang & Chu, Chengbin & Châtelet, Ėric & Yalaoui, Farouk, 2007. "Reliability optimization of a redundant system with failure dependencies," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1627-1634.
    7. Kumar, Pankaj & Jain, Madhu, 2020. "Reliability analysis of a multi-component machining system with service interruption, imperfect coverage, and reboot," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    8. Wu, Hui & Li, Yan-Fu & Bérenguer, Christophe, 2020. "Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Peiravi, Abdossaber & Karbasian, Mahdi & Ardakan, Mostafa Abouei & Coit, David W., 2019. "Reliability optimization of series-parallel systems with K-mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 17-28.
    10. Madhu Jain & Ritu Gupta, 2012. "Load sharing M-out of-N: G system with non-identical components subject to common cause failure," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(5), pages 586-605.
    11. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    12. Sharifi, Mani & Taghipour, Sharareh & Abhari, Abdolreza, 2021. "Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    13. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    14. Li, Chun-yang & Chen, Xun & Yi, Xiao-shan & Tao, Jun-yong, 2010. "Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 202-207.
    Full references (including those not matched with items on IDEAS)

    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. Gao, Shan & Wang, Jinting & Zhang, Jie, 2023. "Reliability analysis of a redundant series system with common cause failures and delayed vacation," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    2. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    3. Cheng, Dawei & Lu, Zhong & Zhou, Jia & Liang, Xihui, 2023. "An optimizing maintenance policy for airborne redundant systems operating with faults by using Markov process and NSGA-II," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    4. Sharifi, Mani & Taghipour, Sharareh & Abhari, Abdolreza, 2021. "Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    5. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    6. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    7. Zhang, Jinchun & Lv, Hang & Hou, Jinxiu, 2023. "A novel general model for RAP and RRAP optimization of k-out-of-n:G systems with mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    8. Guo, Linhan & Li, Ruiyang & Wang, Yu & Yang, Jun & Liu, Yu & Chen, Yiming & Zhang, Jianguo, 2023. "Availability for multi-component k-out-of-n: G warm-standby system in series with shut-off rule of suspended animation," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    9. Ardakan, Mostafa Abouei & Talkhabi, Sajjad & Juybari, Mohammad N., 2022. "Optimal activation order vs. redundancy strategies in reliability optimization problems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    10. Peiravi, Abdossaber & Nourelfath, Mustapha & Zanjani, Masoumeh Kazemi, 2022. "Universal redundancy strategy for system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    11. Qin, Shuidan & Wang, Bing Xing & Tsai, Tzong-Ru & Wang, Xiaofei, 2023. "The prediction of remaining useful lifetime for the Weibull k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    12. He, Gang & Wu, Wenqing & Zhang, Yuanyuan, 2018. "Analysis of a multi-component system with failure dependency, N-policy and vacations," Operations Research Perspectives, Elsevier, vol. 5(C), pages 191-198.
    13. Zheng, Xiaohu & Yao, Wen & Xu, Yingchun & Wang, Ning, 2024. "Algorithms for Bayesian network modeling and reliability inference of complex multistate systems with common cause failure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    14. Liu, Yongchao & Wang, Guanjun & Liu, Peng, 2024. "A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    15. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2017. "Maintenance analysis of a two-component load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 67-74.
    16. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    17. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    18. Ardakan, Mostafa Abouei & Amini, Hanieh & Juybari, Mohammad N., 2022. "Prescheduled switching time: A new strategy for systems with standby components," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    19. Wang, Chaonan & Xing, Liudong & Su, Yujie & Guan, Quanlong & Tang, Bo & Hu, Yuliang, 2023. "Reliability analysis of dynamic voting phased-mission systems," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    20. Brown, Bodunrin & Liu, Bin & McIntyre, Stuart & Revie, Matthew, 2022. "Reliability analysis of load-sharing systems with spatial dependence and proximity effects," Reliability Engineering and System Safety, Elsevier, vol. 221(C).

    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:matcom:v:208:y:2023:i:c:p:637-659. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.