Uncertainty Analysis of Fault-Tree Outputs

The multiaffine nature of the top-event probability as a function of component unavailability is recognized. This leads, under the gssumption of statistically independent failures, to the derivation of an exact formula relating the variance of the system unavailability to the variances of the component unavailability. Concise expressions for other central moments of the system unavailability are obtained. The variance formula partitions contributions due to the input variables and their interactions, and can be used to rank these variables by an importance that is related to well known measures of statistical importance. The variance formula is extended to handle linearly correlated input variables through the inclusion of certain joint central moment terms.