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Analysis for a two-dissimilar-component cold standby repairable system with repair priority

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  • Leung, Kit Nam Francis
  • Zhang, Yuan Lin
  • Lai, Kin Keung

Abstract

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. Assume that working time distributions and repair time distributions of the two components are both exponential, and Component 1 has repair priority when both components are broken down. After repair, Component 1 follows a geometric process repair while Component 2 obeys a perfect repair. Under these assumptions, using the perfect repair model, the geometric process repair model and the supplementary variable technique, we not only study some important reliability indices, but also consider a replacement policy T, under which the system is replaced when the working age of Component 1 reaches T. Our problem is to determine an optimal policy Tâ Ž such that the long-run average loss per unit time (i.e. average loss rate) of the system is minimized. The explicit expression for the average loss rate of the system is derived, and the corresponding optimal replacement policy Tâ Ž can be found numerically. Finally, a numerical example for replacement policy T is given to illustrate some theoretical results and the model's applicability.

Suggested Citation

  • Leung, Kit Nam Francis & Zhang, Yuan Lin & Lai, Kin Keung, 2011. "Analysis for a two-dissimilar-component cold standby repairable system with repair priority," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1542-1551.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:11:p:1542-1551
    DOI: 10.1016/j.ress.2011.06.004
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    References listed on IDEAS

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    5. Zhang, Yuan Lin, 2007. "A discussion on "A bivariate optimal replacement policy for a repairable system"," European Journal of Operational Research, Elsevier, vol. 179(1), pages 275-276, May.
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    3. Guan Jun Wang & Yuan Lin Zhang, 2016. "Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1021-1031, April.
    4. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    5. 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).
    6. Rohit Patawa & Pramendra Singh Pundir & Alok Kumar Sigh & Abhinav Singh, 2022. "Some inferences on reliability measures of two-non-identical units cold standby system waiting for repair," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 172-188, February.
    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 & 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.
    9. 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.
    10. 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.
    11. Eryilmaz, Serkan, 2012. "On the mean residual life of a k-out-of-n:G system with a single cold standby component," European Journal of Operational Research, Elsevier, vol. 222(2), pages 273-277.

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