Probabilistic Model of System Operation with a Varying Degree of Spares and Service Facilities

The techniques for evaluating the probabilistic properties of systems having identical operational and spare units with different facilities for repairs are discussed in this paper. The important properties studied are (a) Reliability and transient behavior of systems, (b) the expected values of times to failures and the measure of variations from the distributions of system failures, and (c) asymptotic or steady-state probability of such a system being in unavailable state. The general expressions are obtained for many cases, while the methods are illustrated by a simple practical example.