Reliability of a Repairable System with Standby Failure

This paper deals with a system in which one unit is operating online and is backed my m spares as warm standbys. There are r repair facilities. The on-line unit has an arbitrary lifetime distribution, while the spares have exponential failure time distributions. The repair time distribution is also exponential. This problem, viewed as a queuing problem, cannot be solved; but by locating a set of renewal points, we write the equations governing the states of the system and calculate the reliability and availability. Explicit results are obtained in the case of five redundant units and three repair facilities.