Variance reduction techniques for uncertainty analysis of fault trees

Abstract

Monte Carlo simulation method has been widely used for the uncertainty propagation analysis in fault tree analysis. It requires a large number of computer runs to generate accurate estimates. Thus variance reduction techniques should be used to improve the simulation efficiency. Estimator accuracy and computation time are equally important to efficiency comparisons of Monte Carlo methods. The purpose of this study is to apply two variance reduction techniques, antithetic variate sampling and Latin hypercube sampling, to the Monte Carlo method for the uncertainty analysis of fault trees and to compare these techniques with the crude Monte Carlo sampling method with respect to computational efficiency. The results of the example problems demonstrated that the variance reduction techniques always provide more accurate estimates than the crude random sampling. Although the Latin hypercube sampling is most effective in reducing the variances, it usually requires highest computer time and storage requirements. For the uncertainty propagation analysis of large fault trees in nuclear power plant safety studies, the antithetic variate sampling is the more efficient variance reduction technique, because it requires the least CPU time and provides at the same time significant variance reduction.