IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v266y2018i3p1189-1197.html
   My bibliography  Save this article

Heterogeneous standby systems with shocks-driven preventive replacements

Author

Listed:
  • 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 and operating components are exposed to external shocks. The components’ resilience to shocks decreases with the number of experienced shocks. A preventive replacement policy when the operating component is replaced after it survives a certain number of shocks is considered. A numerical algorithm for evaluating the expected mission costs and the mission success probability is suggested. An optimization problem for a replacement policy that minimizes the expected mission cost providing a desired level of a mission success probability is formulated and solved. Illustrative examples are provided.

Suggested Citation

  • Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:3:p:1189-1197
    DOI: 10.1016/j.ejor.2017.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717309955
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.11.002?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. 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.
    2. 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.
    3. 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.
    4. Gregory Levitin & Maxim Finkelstein, 2017. "A new stress–strength model for systems subject to stochastic shocks," Journal of Risk and Reliability, , vol. 231(2), pages 172-179, April.
    5. 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.
    6. 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.
    7. Finkelstein, Maxim, 2007. "Shocks in homogeneous and heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 569-574.
    8. Ruiz-Castro, Juan Eloy, 2016. "Complex multi-state systems modelled through marked Markovian arrival processes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 852-865.
    9. Levitin, Gregory & Xing, Liudong & Amari, Suprasad V. & Dai, Yuanshun, 2013. "Reliability of non-repairable phased-mission systems with propagated failures," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 218-228.
    10. Kenné, Jean-Pierre & Gharbi, Ali, 2018. "Production and replacement policies for a deteriorating manufacturing system under random demand and qualityAuthor-Name: Ouaret, Samir," European Journal of Operational Research, Elsevier, vol. 264(2), pages 623-636.
    11. Zhao, Peng & Zhang, Yiying & Chen, Jianbin, 2017. "Optimal allocation policy of one redundancy in a n-component series system," European Journal of Operational Research, Elsevier, vol. 257(2), pages 656-668.
    12. Caserta, Marco & Voß, Stefan, 2015. "An exact algorithm for the reliability redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 110-116.
    13. 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.
    14. 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.
    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. 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.
    2. 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).
    3. 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).
    4. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2021. "Optimal operation and maintenance scheduling in m-out-of-n standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    5. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2021. "Influence of storage on mission success probability of m-out-of-n standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    6. Levitin, Gregory & Xing, Liudong & Dai, Yanshun, 2022. "Minimum cost replacement and maintenance scheduling in dual-dissimilar-unit standby systems," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    7. Eryilmaz, Serkan, 2021. "Revisiting discrete time age replacement policy for phase-type lifetime distributions," European Journal of Operational Research, Elsevier, vol. 295(2), pages 699-704.
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Predetermined standby mode transfers in 1-out-of-N systems with resource-constrained elements," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    9. Li, Yijia & Hu, Xiaoxiao & Zhao, Peng, 2021. "On the reliability of a voting system under cyber attacks," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. 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).
    11. Zhou, Yu & Kou, Gang & Xiao, Hui & Peng, Yi & Alsaadi, Fawaz E., 2020. "Sequential imperfect preventive maintenance model with failure intensity reduction with an application to urban buses," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    12. 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).
    13. 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).
    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).

    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. 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.
    2. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
    3. Levitin, Gregory & Xing, Liudong & Peng, Sun & Dai, Yuanshun, 2015. "Optimal choice of standby modes in 1-out-of-N system with respect to mission reliability and cost," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 587-596.
    4. Levitin, Gregory & Xing, Liudong & Luo, Liang, 2019. "Influence of failure propagation on mission abort policy in heterogeneous warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 29-38.
    5. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2018. "Co-optimization of state dependent loading and mission abort policy in heterogeneous warm standby systems," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 151-158.
    6. Levitin, Gregory & Xing, Liudong & Haim, Hanoch Ben & Dai, Yuanshun, 2019. "Optimal structure of series system with 1-out-of-n warm standby subsystems performing operation and rescue functions," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 523-531.
    7. Heping Jia & Rui Peng & Yi Ding & Yonghua Song, 2019. "Reliability of demand-based warm standby system with common bus performance sharing," Journal of Risk and Reliability, , vol. 233(4), pages 580-592, August.
    8. 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).
    9. 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.
    10. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    11. Huang, Yeu-Shiang & Fang, Chih-Chiang & Lu, Chang-Ming & (Bill) Tseng, Tzu-Liang, 2022. "Optimal Warranty Policy for Consumer Electronics with Dependent Competing Failure Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    12. 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).
    13. 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).
    14. Chen, Yiming & Liu, Yu & Jiang, Tao, 2021. "Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    15. Li, Yan & Cui, Lirong & Lin, Cong, 2017. "Modeling and analysis for multi-state systems with discrete-time Markov regime-switching," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 41-49.
    16. 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.
    17. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2018. "Optimal work distribution and backup frequency for two non-identical work sharing elements," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 127-136.
    18. 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).
    19. Reihaneh, Mohammad & Abouei Ardakan, Mostafa & Eskandarpour, Majid, 2022. "An exact algorithm for the redundancy allocation problem with heterogeneous components under the mixed redundancy strategy," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1112-1125.
    20. Ruiz-Castro, Juan Eloy, 2016. "Complex multi-state systems modelled through marked Markovian arrival processes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 852-865.

    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:ejores:v:266:y:2018:i:3:p:1189-1197. 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.elsevier.com/locate/eor .

    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.