# A new kind of repairable system with repairman vacations

Volume 8, Issue 4, pp 324--333
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### Authors

Xiao Zhang - Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, P. R. China. Lina Guo - Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China.

### Abstract

In this paper, a new kind of series repairable system with repairman vacation is discussed, in which the failure rate functions of all the units and the delayed vacation rate function of the repairman are related to the working time of the system. The system model of a group of integro-differential equations is established by using probability analysis method, which then is translated into an initial value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further study. Then the conditions of the existence and uniqueness of the system solution is analyzed by using $C_0$-semigroup theory. And by using Laplace transform method, some steady-state reliability indexes, such as system availability, failure frequency, and the probability that the repairman is on vacation, are discussed. Numerical examples are also presented at the end of the paper.

### Share and Cite

##### ISRP Style

Xiao Zhang, Lina Guo, A new kind of repairable system with repairman vacations, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 4, 324--333

##### AMA Style

Zhang Xiao, Guo Lina, A new kind of repairable system with repairman vacations. J. Nonlinear Sci. Appl. (2015); 8(4):324--333

##### Chicago/Turabian Style

Zhang, Xiao, Guo, Lina. "A new kind of repairable system with repairman vacations." Journal of Nonlinear Sciences and Applications, 8, no. 4 (2015): 324--333

### Keywords

• Repairable system
• delayed-multiple vacations
• semi-linear evolution system
• $C_0$-semigroup theory
• well-posedness
• stability
• sensitivity analysis.

•  47H10
•  54H25

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