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An optimal replacement policy for a repairable system based on its repairman having vacations

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  • Yuan, Li
  • Xu, Jian

Abstract

This paper studies a cold standby repairable system with two different components and one repairman who can take multiple vacations. If there is a component which fails and the repairman is on vacation, the failed component will wait for repair until the repairman is available. In the system, assume that component 1 has priority in use. After repair, component 1 follows a geometric process repair, while component 2 can be repaired as good as new after failures. Under these assumptions, a replacement policy N based on the failed times of component 1 is studied. The system will be replaced if the failure times of component 1 reach N. The explicit expression of the expected cost rate is given, so that the optimal replacement time Nâ Ž is determined. Finally, a numerical example is given to illustrate the theoretical results of the model.

Suggested Citation

  • Yuan, Li & Xu, Jian, 2011. "An optimal replacement policy for a repairable system based on its repairman having vacations," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 868-875.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:7:p:868-875
    DOI: 10.1016/j.ress.2011.02.004
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Yuan Lin & Wang, Guan Jun, 2007. "A deteriorating cold standby repairable system with priority in use," European Journal of Operational Research, Elsevier, vol. 183(1), pages 278-295, November.
    3. de Smidt-Destombes, Karin S. & van der Heijden, Matthieu C. & van Harten, Aart, 2007. "Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 404-421, June.
    4. 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.
    5. Yeo, Wee Meng & Yuan, Xue-Ming, 2009. "Optimal warranty policies for systems with imperfect repair," European Journal of Operational Research, Elsevier, vol. 199(1), pages 187-197, November.
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    Cited by:

    1. 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.
    2. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Optimal loading of system with random repair time," European Journal of Operational Research, Elsevier, vol. 247(1), pages 137-143.
    3. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
    4. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    5. An, Youjun & Chen, Xiaohui & Hu, Jiawen & Zhang, Lin & Li, Yinghe & Jiang, Junwei, 2022. "Joint optimization of preventive maintenance and production rescheduling with new machine insertion and processing speed selection," Reliability Engineering and System Safety, Elsevier, vol. 220(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. Yu, Miaomiao & Tang, Yinghui & Liu, Liping & Cheng, Jiang, 2013. "A phase-type geometric process repair model with spare device procurement and repairman’s multiple vacations," European Journal of Operational Research, Elsevier, vol. 225(2), pages 310-323.
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Optimal backup frequency in system with random repair time," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 12-22.

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