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

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.