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Journal of Applied Mathematics
Volume 2012, Article ID 182975, 16 pages
Research Article

A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 15 April 2012; Accepted 7 May 2012

Academic Editor: Francis T. K. Au

Copyright © 2012 Renbin Liu and Yong Wu. 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.


Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in an n-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during (0,t] of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.