Based on the renewal process theory we develop a decomposition method to analyze the German Martingale 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, Toys two convolution relations.Special cases and numerical examples are given to show the validity of our method.