A new kind of repairable system with repairman vacations
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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.
MSC
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