Probabilistic Analysis of a System with Two Dissimilar Units Subject to Preventive Maintenance and a Single Service Facility

This paper deals with the availability and the reliability analysis of a system consisting of two dissimilar units having a single service facility and subject to preventive maintenance. The times to failure, the repair times, and the preventive maintenance times of the units are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. By identifying suitable regenerative stochastic processes, we derive integral equations for these probabilities corresponding to different initial conditions, and we use Laplace transform technique to solve the equations. Explicit expressions for the mean down-time of the system during the period (0, t) and for the mean-time-to-system-failure are obtained. The case when the system is not subject to preventive maintenance is considered as a particular case.