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A new repair model and its optimization for cold standby system

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Abstract

In this paper, we propose a new repair model for a cold standby system, which consists of two components and one repairman. It is assumed that the consecutive working time follows decreasing geometric process after repair, and the repair time interval is a constant for component 1. For component 2 (standby component), the failure process during working time follows Generalized Polya Process, which is a generalized version of the nonhomogeneous Poisson process. Component 2 is rectified by Generalized Polya Process repair when it fails. The repair time of component 2 is assumed to be negligible. Component 1 is assumed to have priority in use. The long-run average cost rate function of the system is deduced based on the failure number of component 1. Moreover, the optimal replacement policy of model is established by minimizing the long-run average cost rate function theoretically, which proves the existence and uniqueness of the optimal replacement policy. Numerical examples are provided to verify the effectiveness of the proposed approaches. Sensitivity analysis are conducted to illustrate the influence of parameters under the optimal replacement policy.

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Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant number [61573014] and the Fundamental Research Funds for the Central Universities of China under Grant number [JB180702]. The authors would like to thank the editor and the anonymous referees for the valuable suggestions that improved the quality of this paper.

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  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Junyuan Wang & Jimin Ye

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  1. Junyuan Wang
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  2. Jimin Ye
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Correspondence to Jimin Ye.

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This work was supported by National Natural Science Foundation of China [Grant number 61573014] and the Fundamental Research Funds for the Central Universities of China [Grant Number JB180702].

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Wang, J., Ye, J. A new repair model and its optimization for cold standby system. Oper Res Int J 22, 105–122 (2022). https://doi.org/10.1007/s12351-020-00545-x

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