A Robust and Efficient Algorithm for Reliability Assessment of Phased-Mission Systems

The operation of missions encountered in aerospace, defense, and many other advanced applications often involves different tasks or phases that must be accomplished in sequence. Systems used in these missions are called phase-dmission systems (PMS). During each mission phase, the system must accomplish a specified set of tasks and may be subject to different operational stresses and environmental conditions as well as different reliability requirements. Thus, system configuration, success criteria, and component failure behavior may change from phase to phase. In addition, an accurate reliability analysis of these systems must consider the statistical dependencies of component states across the phases. The consideration of these dynamic dependencies poses unique challenges to existing reliability analysis methods. In this paper, we propose a robust and efficient algorithm for exact reliability assessment of a special structured phased mission systems consisting of several subsystems. The subsystems and the components within each subsystem can be non-identical. From the published examples based on real applications, it is shown that the special structure considered in this paper is applicable for a wide range of practical systems. We also considered a special case of the proposed model where the components within a subsystem are divided into two nonidentical sub-groups each consisting of identical components. The solution is provided considering time-varying and phasedependent failure rates and associated cumulative damage effects. The proposed algorithm is based on (1) modularization techniques, (2) conditional probabilities, and (3) efficient recursive formulas to compute these conditional probabilities. The main advantage of this algorithm is that both the computational time and memory requirements are linear in number of phases and pseudo-polynomial in the system size. The numerical examples demonstrate that the proposed algorithm provides a robust, efficient, and accurate reliability analysis of practical and large-scale phased-mission systems.