Modular model and algebraic phase algorithm for reliability modelling and evaluation of phased-mission systems with conflicting phase redundancy

Phased-mission systems (PMSs) have been widely used as mission reliability models for many complex systems whose missions can be divided into several phases. In practice, PMSs may have conflicting phase redundancy, that is, a phase task can be performed in more than one phase and redundancy phases can be shared by more than one failed phase. Such PMSs have the following characteristics: (1) the failure of a phase task with redundancy does not directly lead to the failure of the system mission; (2) they have more than one phase level path; and (3) redundancy phases of them have multiple states. This study investigates the reliability modelling and evaluation method of such PMSs with conflicting phase redundancy (PMS-PR). A modular model with new phase states notes was provided to depict the states of phases and deal with the redundant conflicts. A general phase algebraic algorithm is provided to produce all the disjoint phase level paths for the PMS-PR based on the presented model. The mission reliability PMS-PR can be estimated based on disjoint phase level paths. Finally, a simplified telemetry, tracking, and command system under different phase redundancy strategies is analysed to illustrate the effectiveness of the model and algorithm.