A Simple Repairable System with Warning Device. (25th June 2015)

• Record Type: Journal Article
• Authors: Zhang, Xiao; Guo, Lina
• Other Names: Chung Jaeyoung Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-06-25
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/671756
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory orC 0 semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper.