Event group importance measures for top event frequency analyses

Three traditional importance measures, risk reduction, partial derivative, nd variance reduction, have been extended to permit analyses of the relative importance of groups of underlying failure rates to the frequencies of resulting top events. The partial derivative importance measure was extended by assessing the contribution of a group of events to the gradient of the top event frequency. Given the moments of the distributions that characterize the uncertainties in the underlying failure rates, the expectation values of the top event frequency, its variance, and all of the new group importance measures can be quantified exactly for two familiar cases: (1) when all underlying failure rates are presumed independent, and (2) when pairs of failure rates based on common data are treated as being equal (totally correlated). In these cases, the new importance measures, which can also be applied to assess the importance of individual events, obviate the need for Monte Carlo sampling. The event group importance measures are illustrated using a small example problem and demonstrated by applications made as part of a major reactor facility risk assessment. These illustrations and applications indicate both the utility and the versatility of the event group importance measures