A numerical analysis of dynamic fault trees based on stochastic bounds

Abstract

We present a numerical method based on stochastic bounds and computations of discrete distributions to get the transient reliability of a system described by a Dynamic Fault Tree. We show that the gates of the tree are associated to simple operators on the probability distributions of the time to failure. We also prove that almost all operators are stochastically monotone, which allows us to simplify the computation complexity using stochastic bounds. We show that replicated events and functional dependency gates can be analyzed with conditional probabilities which can be handled with the same techniques but with a higher complexity. Finally we show the tradeoff between the precision of the approach and the complexity of the computations.