A new approach for analyzing the reliability of the repair facility in a series system with vacations (Q1760584)

Summary: 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.