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An analytical method is presented which enables one to propagate uncertainties described by continuous probability density functions through fault trees from the lower level (basic event) to the higher level (top-event) of a stochastic binary system. It is based on calculating the expected value and the variance of the top-event probability by means of Binary Decision Diagrams (BDD). This method allows an accurate computation of both the expected value and the variance of the top-event probability. We show, on a benchmark of real fault trees, that our method results in a quantitative and qualitative improvement in safety analysis of industrial systems, especially those concerning accurate evaluation of Safety Integrity Levels (SIL), whenever different sources of uncertainties are present. The numerical results of the analytical method are in good agreement with those of the Monte Carlo method.