Analyses of Two Different 1-Server Systems

In this paper, the availability and the reliability of two 1-server systems with redundancy have been obtained. System 1 consists of n subsystems in series; each subsystem consists of two redundant i.i.d. components in `parallel´ (cold standby) and one server. The times to failure of the components are exponentially distributed; their repair time distributions are arbitrary and different. System 2 consists of n dissimilar units and one server. The times to failure of the units are arbitrarily distributed; the repair rates are constant but all different. Explicit expressions for the Laplace transform of the mean down-time of the system in (0, t) and for the mean time to system failure have been obtained. A few particular cases are discussed.