Variance reduction for estimating a failure probability with multiple criteria

We consider a system subjected to multiple loads with corresponding capacities to withstand the loads, where both loads and capacities are random. The system fails when any load exceeds its capacity, and the goal is to apply Monte Carlo methods to estimate the failure probability. We consider various combinations of variance-reduction techniques, including stratified sampling, conditional Monte Carlo, and Latin hypercube sampling. Numerical results are presented for an artificial safety analysis of a nuclear power plant, which illustrate that the combination of all three methods can greatly increase statistical efficiency.