Reliability of Systems with Time-Varying Coverage

A mathematical model is established for reliability estimation in a modularly redundant system whose coverage depends on the tasks which the system is performing. The system consists of active units plus one spare on warm standby. The mean time-to-system-failure and the Laplace transformn of reliability are obtained. An explicit formula for the reliability is obtained when the ``time for performing a task´´ is a constant. The approximate formulas are very simple and easy to use.