A Time-varying repairable system with repairman vacation and warning device

Volume 9, Issue 1, pp 316--331 http://dx.doi.org/10.22436/jnsa.009.01.30

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Authors

Lina Guo - Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China. Maomao Zhang - Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P. R. China.

Abstract

In this paper, a new kind of repairable system with repairman vacation and warning device is discussed, in which the delayed vacation rate and failure rates are functions related to system working time. The system model is established by using probability analysis method, which then is translated into a initial value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further study. The conditions of the existence and uniqueness of the system solution as well as system stability is analyzed by using \(C_0\)-semigroup theory. Some steady-state reliability indexes are studied by using Laplace transformation. In the end, numerical examples are presented to compare some indexes of the systems with and without warning device.

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Keywords

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

MSC

•  47H10
•  54H25

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