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A geometric process repair model for a repairable cold standby system with priority in use and repair

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  • Zhang, Yuan Lin
  • Wang, Guan Jun

Abstract

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:11:p:1782-1787
    DOI: 10.1016/j.ress.2009.05.009
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    1. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    2. Castro, I.T. & Pérez-Ocón, R., 2006. "Reward optimization of a repairable system," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 311-319.
    3. Zhang, Yuan Lin & Yam, Richard C.M. & Zuo, Ming J., 2007. "A bivariate optimal replacement policy for a multistate repairable system," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 535-542.
    4. Chen, Jinyuan & Li, Zehui, 2008. "An extended extreme shock maintenance model for a deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1123-1129.
    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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    Citations

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    Cited by:

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    2. Wang, Wei & Wu, Zhiying & Xiong, Junlin & Xu, Yaofeng, 2018. "Redundancy optimization of cold-standby systems under periodic inspection and maintenance," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 394-402.
    3. Wenke Gao, 2020. "An extended geometric process and its application in replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 88-103, February.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. Miaomiao Yu & Yinghui Tang, 2017. "Optimal replacement policy based on maximum repair time for a random shock and wear model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 80-94, April.
    10. Junyuan Wang & Jimin Ye & Qianru Ma & Pengfei Xie, 2022. "An extended geometric process repairable model with its repairman having vacation," Annals of Operations Research, Springer, vol. 311(1), pages 401-415, April.
    11. 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.
    12. 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.

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