Geodesic
A new kind of repairable system with repairman vacations
Zhang, Xiao1 ; Guo, Lina2
1 Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, P. R. China
2 Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 4, p. 324-333.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.008.04.05
Classification : 47H10, 54H25
Keywords: Repairable system, delayed-multiple vacations, semi-linear evolution system, \(C_0\)-semigroup theory, well-posedness, stability, sensitivity analysis.

Zhang, Xiao 1 ; Guo, Lina 2

1 Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, P. R. China
2 Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China 
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Zhang, Xiao; Guo, Lina. A new kind of repairable system with repairman vacations. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 4, p. 324-333. doi : 10.22436/jnsa.008.04.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.04.05/

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