A Combinatorial Modeling Method for Mission Reliability of Phased-Mission System With Phase Backups

In many real-world applications, phased-mission systems (PMSs) often have time redundancy in the form of that mission task failed in one phase can be re-executed in a backup phase with change of its configurations. In this case, a new kind of dependence among phase tasks is involved: the success or failure of a phase task may result in a different configuration of its backup phases, and the original task in the backup phase may be either cooperated with or replaced by the failed task. It is essential to consider such redundancy as a more precise result for system mission reliability evaluation is required. This article proposes a combinatorial method to model the mission reliability of PMS with such phase backups. A compressed event tree containing only failure branches is constructed, each branch describing a mission failure cause as an execution sequence of a set of dependent phase tasks. Each phase task is supported by a kind of phase configuration, whose failure causes are modeled by a fault tree illustrating the logic relations of component malfunctions. A binary decision diagram-based method is applied on this combinatorial model to calculate the mission failure probability, and always has a better performance than other alternative solutions. Examples are analyzed for illustration, and the results show the effectiveness of the proposed approach.