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A bivariate optimal replacement policy for a multistate repairable system

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  • Zhang, Yuan Lin
  • Yam, Richard C.M.
  • Zuo, Ming J.

Abstract

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new†and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)* is better than the optimal policy N* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:4:p:535-542
    DOI: 10.1016/j.ress.2006.01.018
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    References listed on IDEAS

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    1. Lam, Yeh & Zhang, Yuan Lin & Zheng, Yao Hui, 2002. "A geometric process equivalent model for a multistate degenerative system," European Journal of Operational Research, Elsevier, vol. 142(1), pages 21-29, October.
    2. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    3. Y L Zhang & R C M Yam & M J Zuo, 2002. "Optimal replacement policy for a multistate repairable system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(3), pages 336-341, March.
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    Cited by:

    1. Zhao, Xufeng & Mizutani, Satoshi & Nakagawa, Toshio, 2015. "Which is better for replacement policies with continuous or discrete scheduled times?," European Journal of Operational Research, Elsevier, vol. 242(2), pages 477-486.
    2. 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).
    3. 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.
    4. Hanagal David D. & Kanade Rupali A., 2010. "Optimal Replacement Policy Based on the Number of Down Times with Priority in Use," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 243-251, January.
    5. Zhao, Xufeng & Liu, Hu-Chen & Nakagawa, Toshio, 2015. "Where does “whichever occurs first†hold for preventive maintenance modelings?," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 203-211.
    6. 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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