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Optimal design of a general warm standby system

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  • Yun, Won Young
  • Cha, Ji Hwan

Abstract

Redundancy or standby is a technique that has been widely applied to improving system reliability and availability in the stage of system design. In this paper, we consider a standby system with two units in which the first unit (unit 1) starts its operation under active state and the other unit (unit 2) is under cold standby state at the starting point. After a specified time s (switching time), the state of unit 2 is changed to warm standby state and, as soon as the operating unit 1 fails, the state of unit 2 is changed to active state. If unit 1 fails before time s, the system fails. Units can fail at both active and warm standby states. A general method for modeling the standby system is adopted and system performance measures (system reliability and mean life) based on the proposed model are derived. Three models – a perfect switching model and two imperfect switching models – are considered in this paper. Two imperfect switching models include an imperfect switching probability and a preliminary warm-up period which is required for the change from cold standby state to warm standby state. We consider the problem of determining the optimal switching time which maximizes the expected system life and related allocation problem is also discussed. Some numerical examples are studied.

Suggested Citation

  • Yun, Won Young & Cha, Ji Hwan, 2010. "Optimal design of a general warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 880-886.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:8:p:880-886
    DOI: 10.1016/j.ress.2010.03.004
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    References listed on IDEAS

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    1. Ji Hwan Cha & Jie Mi & Won Young Yun, 2008. "Modelling a general standby system and evaluation of its performance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(2), pages 159-169, March.
    2. Zhang, Yuan Lin & Wang, Guan Jun, 2009. "A geometric process repair model for a repairable cold standby system with priority in use and repair," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1782-1787.
    3. 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.
    4. Yu, Haiyang & Yalaoui, Farouk & Châtelet, Ėric & Chu, Chengbin, 2007. "Optimal design of a maintainable cold-standby system," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 85-91.
    5. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, December.
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    Cited by:

    1. Peng, Rui & Zhai, Qingqing & Xing, Liudong & Yang, Jun, 2014. "Reliability of demand-based phased-mission systems subject to fault level coverage," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 18-25.
    2. 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).
    3. Zohreh Pakdaman & Jafar Ahmadi, 2019. "Switching time of the standby component to the k-out-of-n:G system in the stress–strength setup," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 225-248, March.
    4. Levitin, Gregory & Jia, Heping & Ding, Yi & Song, Yonghua & Dai, Yuanshun, 2017. "Reliability of multi-state systems with free access to repairable standby elements," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 192-197.
    5. Kundu, Pradip & Hazra, Nil Kamal & Nanda, Asok K., 2016. "Reliability study of a coherent system with single general standby component," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 25-33.
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Heterogeneous 1-out-of-n standby systems with limited unit operation time," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    7. Wells, Charles E., 2014. "Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures," European Journal of Operational Research, Elsevier, vol. 235(1), pages 180-186.
    8. E. Vanderperre & S. Makhanov, 2015. "Reliability of Birolini’s duplex system sustained by a cold standby unit and subjected to a priority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 441-465, July.
    9. Xiaoyu Zhang & Yiying Zhang & Rui Fang, 2020. "Allocations of cold standbys to series and parallel systems with dependent components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(3), pages 432-451, May.
    10. Qingqing Zhai & Rui Peng & Liudong Xing & Jun Yang, 2013. "Binary decision diagram-based reliability evaluation of k-out-of-(n + k) warm standby systems subject to fault-level coverage," Journal of Risk and Reliability, , vol. 227(5), pages 540-548, October.
    11. E.J. Vanderperre & S.S. Makhanov, 2014. "Reliability analysis of a repairable duplex system," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(9), pages 1970-1977, September.
    12. Min Gong & Hanlin Liu & Rui Peng, 2020. "Redundancy allocation of mixed warm and cold standby components in repairable K-out-of-N systems," Journal of Risk and Reliability, , vol. 234(5), pages 696-707, October.
    13. Jia, Xiang & Chen, Hao & Cheng, Zhijun & Guo, Bo, 2016. "A comparison between two switching policies for two-unit standby system," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 109-118.
    14. Edmond Vanderperre & Stanislav Makhanov, 2014. "On the availability of a warm standby system: a numerical approach," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 644-657, July.
    15. Wang, Chaonan & Xing, Liudong & Amari, Suprasad V., 2012. "A fast approximation method for reliability analysis of cold-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 119-126.

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