Estimating a failure probability using a combination of variance-reduction techniques

Consider a system that is subjected to a random load and having a corresponding random capacity to withstand the load. The system fails when the load exceeds capacity, and we consider efficient simulation methods for estimating the failure probability. Our approaches employ various combinations of stratified sampling, Latin hypercube sampling, and conditional Monte Carlo. We construct asymptotically valid upper confidence bounds for the failure probability for each method considered. We present numerical results to evaluate the proposed techniques on a safety-analysis problem for nuclear power plants, and the simulation experiments show that some of our combined methods can greatly reduce variance.