Modelling and analysis of repairable systems with preventive maintenance

The time-dependent solution of a kind of repairable system with preventive maintenance is investigated in the paper. With total probability formula, we show that the behavior of the system can be described as a group of ordinary differential equations coupled with partial differential equations, which can be formulated as a time delay equation in an appropriate Banach space. Based on the time-delay equation, this paper presents a difference scheme as an approximating method to solve the time-dependent solution which is necessary for analyzing the instantaneous availability of the repairable system. Some numerical examples are shown to illustrate the effectiveness of this approach.