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Reliability analysis of a cold standby repairable system with repairman extra work

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Abstract

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C 0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

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Authors and Affiliations

  1. Department of Basic Courses, Beijing Union University, Beijing, 100101, China

    Xin Zhang

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xin Zhang

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  1. Xin Zhang
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Correspondence to Xin Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11201007.

This paper was recommended for publication by Editor WANG Shouyang.

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Zhang, X. Reliability analysis of a cold standby repairable system with repairman extra work. J Syst Sci Complex 28, 1015–1032 (2015). https://doi.org/10.1007/s11424-015-4081-5

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  • DOI: https://doi.org/10.1007/s11424-015-4081-5

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