Reliability Analysis of Hierarchical Systems Using Statistical Moments

In many practical engineering circumstances, systems reliability analysis is complicated by the fact that the failure time distributions of the constituent subsystems cannot be accurately modeled by standard distributions. In this paper, we present a low-cost, compositional approach based on the use of the first four statistical moments to characterize the failure time distributions of the constituent components, subsystems, and top-level system. The approach is based on the use of Pearson distributions as an intermediate analytical vehicle, in terms of which the constituent failure time distributions are approximated. The analysis technique is presented for -out-of- systems with identical subsystems, series systems with different subsystems, and systems exploiting standby redundancy. The moment-in-moment-out approach allows for the analysis of systems with arbitrary hierarchy, and arbitrary (unimodal) failure time distributions, provided the subsystems are independent such that the resulting failure time can be expressed in terms of sums or order statistics. The technique consistently exhibits very good accuracy (on average, much less than 1 percent error) at very modest computing cost.