Unavailability analysis of periodically tested standby components

General recursive models are developed for the unavailability and the mission-failure probability of standby equipment subject to periodic testing. The analytic approach allows general distributions for the failure times, test durations, and repair times. It accounts for start-up failures, standby failures, and failures during mission, as well as several categories of human error. Explicit expressions are derived for the unavailabilities and approximate optimal test-intervals for constant standby failure rate