In this paper an efficient procedure for calculating non-exceedance probabilities of the structural response is presented, with emphasis on structures modeled by large finite element systems with many uncertain parameters. This is a problem which receives considerable attention in numerous applications of engineering mechanics, such as space and aerospace engineering. For this purpose, a novel sampling procedure is introduced, which allows a significant reduction of the variance of the estimator of the probability of failure when compared to that of direct Monte Carlo simulation. This improvement in the computational efficiency is most important, as the computational efforts are much higher when uncertainties are considered.

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