FINDING THE EXACT TOP EVENT UNAVAILABILITY MEAN AND VARIANCE EXPRESSIONS OF FAULT-TREES HAVING CORRELATED JOINTLY LOGNORMAL COMPONENT FAILURE PROBABILITIES

This paper describes related extensions to two methods. One method is given by Apostolakis and Lee 1 and uses minimal cut-sets and Taylor Series expansions to estimate the mean and variance of the top-event unavailability (probability of being unavailable) of fault trees. The other method is given by Zhang 2 for estimating the mean and variance with Monte Carlo when the component unavailability distributions are correlated and the correlations are decomposable. The extensions produce analysable expressions that handle correlated component unavailability probabilities. The expressions are exact when, as is often done,1,3 the component unavailability probabilities are modeled using jointly lognormal distributions. For Zhang, an added condition for exactness is that the decomposition is in terms of products of exponentiated underlying lognormal random variables.