Unreliability of a Standby System with Repair and Imperfect Switching

We evaluate and analyze a model of a 2-unit standby system with repair and imperfect switching. The model determines the cumulative probability that system failure occurs in a time interval 0 to T. In order to cope with arbitrary failure-time and repair-time distributions, a ``step by step' method is used which for practical purposes yields a sufficiently accurate result. The model results in explicit expressions which are very suitable for computer implementation. A simple illustrative example is given.