Probabilistic competing failure analysis in phased-mission systems

Many real-world systems are classified as phased-mission systems (PMSs). These systems involve multiple, consecutive, non-overlapping phases of operations, where system configuration and component behavior can vary from phase to phase due to changing tasks and environmental conditions. In addition, statistical dependencies exist across phases for a given component. These dynamic, dependent behaviors make reliability analysis of PMSs more challenging than single-phase systems. Further complicating the PMS analysis is the probabilistic functional dependence behavior where operations of some system components (referred to as probabilistic-dependent components) rely on functions of other components (referred to as trigger components) with certain probabilities. Time-domain competitions exist between a trigger component failure and propagated failures of related probabilistic-dependent components; different occurrence sequences can cause distinct system statuses. This paper models effects of phase-dependent, probabilistic competing failures, and suggests a multiple-valued decision diagram-based combinatorial procedure for reliability analysis of non-repairable PMSs. The method is applicable to arbitrary types of time-to-failure distributions for system components and probabilistic isolation factors, as well as different statistical relationships between local and propagated failures of the same component. A case study is presented to illustrate applications and advantages of the proposed method. Correctness of the method is verified using Monte Carlo simulations.