Reliability Analysis of kout-of-n Systems with Phased-Mission Requirements

Many practical systems are phased-mission systems (PMS) where the mission consists of multiple, consecutive, and non-overlapping phases. An accurate reliability analysis of a PMS must consider the statistical dependencies of component states across phases as well as dynamics in system configuration, success criteria and component behavior. In this paper, we propose an efficient method for exact reliability evaluation of k-out-of-n systems with identical components subject to phased-mission requirements where the k values and failure time distributions can change with the phases. We also consider the time-varying and phase-dependent failure rates and associated cumulative damage effects. The proposed method is based on conditional probabilities and an efficient recursive formula to compute these probabilities. The main advantage of this method is that both its computational time and memory requirements are linear in terms of the system size.