Abstract
Phased mission systems (PMSs) complete tasks through multiple, consecutive, non-overlapping phases, with system configuration and component behavior evolving across phases in response to tasks and environmental changes. In PMSs with functional dependence, the sequence of local failures (LFs) of trigger components and propagated failures (PFs) of dependent components creates a time-domain competition between failure propagation and isolation, resulting in distinct system states. Existing reliability models addressing such competitions either assume instantaneous failure isolation or apply only to single-phase systems. To fill this research gap, this work contributes by proposing a combinatorial reliability model for addressing competitions in PMSs with random failure isolation times (ITs). Based on the total probability theorem, the proposed approach implements a divide-and-conquer strategy to decompose the original reliability problem into independent reduced subproblems, integrating multi-valued decision diagrams for addressing cross-phase dependence and sequential event probability evaluation for incorporating random IT and the competition effects. The proposed approach accommodates arbitrary types of time-to-failure and IT distributions. A case study on an unmanned aerial vehicle swarm for air quality monitoring demonstrates the proposed approach and the impacts of random isolation time on PMS reliability. The correctness of the proposed approach is verified using Monte Carlo simulations. By capturing realistic, non-instantaneous failure isolation behavior, the proposed model offers more accurate reliability assessment that can support better-informed design and operation decisions for PMSs.