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Optimizing availability of heterogeneous standby systems exposed to shocks

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  • Levitin, Gregory
  • Finkelstein, Maxim
  • Dai, Yuanshun

Abstract

The paper considers heterogeneous 1-out-of-N warm standby systems when all components can experience internal failures whereas operating components are exposed to the external shocks as well. The components’ resilience to shocks decreases with the number of experienced shocks describing the corresponding deterioration in time. Therefore, a preventive replacement policy when the operating component is replaced after it survives a certain number of shocks (that becomes a decision parameter) is considered. The replacement time is random and not negligible. The distributions of corrective and preventive replacement times are assumed to be known for each component. The expression for the instantaneous (point) availability is derived and the original numerical algorithm for its evaluation is suggested. Then an optimization problem for a replacement policy that maximizes the overall mission availability over a finite time horizon is formulated and solved. Illustrative examples are provided.

Suggested Citation

  • Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Optimizing availability of heterogeneous standby systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 137-145.
    • Handle: RePEc:eee:reensy:v:170:y:2018:i:c:p:137-145
    DOI: 10.1016/j.ress.2017.10.021
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    References listed on IDEAS

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    1. Song, Sanling & Coit, David W. & Feng, Qianmei, 2014. "Reliability for systems of degrading components with distinct component shock sets," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 115-124.
    2. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
    3. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
    4. H. Wang & H. Pham, 1999. "Some maintenance models and availability withimperfect maintenance in production systems," Annals of Operations Research, Springer, vol. 91(0), pages 305-318, January.
    5. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    6. Zhang, Tieling & Xie, Min & Horigome, Michio, 2006. "Availability and reliability of k-out-of-(M+N):G warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 91(4), pages 381-387.
    7. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    8. Finkelstein, Maxim, 2007. "On statistical and information-based virtual age of degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 676-681.
    9. Ruiz-Castro, Juan Eloy & Fernández-Villodre, Gemma, 2012. "A complex discrete warm standby system with loss of units," European Journal of Operational Research, Elsevier, vol. 218(2), pages 456-469.
    10. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    11. Frostig, Esther & Kenzin, Moshe, 2009. "Availability of inspected systems subject to shocks - A matrix algorithmic approach," European Journal of Operational Research, Elsevier, vol. 193(1), pages 168-183, February.
    12. Papageorgiou, Effie & Kokolakis, George, 2010. "Reliability analysis of a two-unit general parallel system with (n-2) warm standbys," European Journal of Operational Research, Elsevier, vol. 201(3), pages 821-827, March.
    13. Kenzin, Moshe & Frostig, Esther, 2009. "M out of n inspected systems subject to shocks in random environment," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1322-1330.
    14. Levitin, Gregory & Finkelstein, Maxim, 2017. "Optimal backup in heterogeneous standby systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 336-344.
    15. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2014. "Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 155-162.
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    Cited by:

    1. Huang, Xianzhen & Jin, Sujun & He, Xuefeng & He, David, 2019. "Reliability analysis of coherent systems subject to internal failures and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 75-83.
    2. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2021. "Optimizing preventive replacement schedule in standby systems with time consuming task transfers," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    3. Xiaoyue Wang & Ru Ning & Xian Zhao, 2023. "Generalized mixed shock model for multi-component systems in the shock environment with a change point," Journal of Risk and Reliability, , vol. 237(4), pages 619-635, August.
    4. Levitin, Gregory & Xing, Liudong & Dai, Yanshun, 2021. "Joint optimal mission aborting and replacement and maintenance scheduling in dual-unit standby systems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    6. 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).
    7. 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).
    8. Fan, Dongming & Sun, Bo & Dui, Hongyan & Zhong, Jilong & Wang, Ziyao & Ren, Yi & Wang, Zili, 2022. "A modified connectivity link addition strategy to improve the resilience of multiplex networks against attacks," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    9. Peng, Rui & He, Xiaofeng & Zhong, Chao & Kou, Gang & Xiao, Hui, 2022. "Preventive maintenance for heterogeneous parallel systems with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    10. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2021. "Optimal multiple replacement and maintenance scheduling in two-unit systems," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    11. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Optimal preventive replacement policy for homogeneous cold standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    12. Junyuan Wang & Jimin Ye, 2022. "A new repair model and its optimization for cold standby system," Operational Research, Springer, vol. 22(1), pages 105-122, March.
    13. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Co-optimizing component allocation and activation sequence in heterogeneous 1-out-of-n standby system exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    14. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    15. 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).
    16. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(C).

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