A new method is presented for propagating uncertainties in complex nuclear power plant safety system fault tree models. The method is especially useful for estimating extreme percentiles and high-probability one-sided confidence intervals of the system unavailability. Likelihood weighing simulation methods, which assign a score to each sample point (x1,... ,xn) to compensate for the differences between the sample and the parent distributions, are used to directly simulate the adequate tail distribution of the probability of the fault tree top event. The polynomial structure of the probability of the top event is exploited to sequentially find upper and lower bounds to simulate each of the basic variables, without the need to invert the polynomial expression. The performance of the proposed method is spectacular when compared with the standard Monte Carlo simulation for tails. Finally, one example of application to a real case is used to illustrate the whole simulation process.