The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method.
Properties of the Weibull cumulative exposure model
