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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 674191, 19 pages
http://dx.doi.org/10.1155/2013/674191
Research Article

Stability Analysis of a Repairable System with Warning Device and Repairman Vacation

Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received 19 April 2013; Accepted 7 August 2013

Academic Editor: Gen-Qi Xu

Copyright © 2013 Yangli Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and uniqueness as well as regularity of the system dynamic solution are discussed with the functional analysis method. Further, the asymptotic stability, especially the exponential stability of the system dynamic solution, is studied by using the strongly continuous semigroup theory or semigroup theory. The reliability indices and some applications (such as the comparisons of indices and profit of systems with and without warning device), as well as numerical examples, are presented at the end of the paper.