Importance Sampling for Reliability Evaluation With Stochastic Simulation Models

Importance sampling has been used to improve the efficiency of simulations where the simulation output is uniquely determined, given a fixed input. We extend the theory of importance sampling to estimate a system's reliability with stochastic simulations. Thanks to the advance of computing power, stochastic simulation models are employed in many applications to represent a complex system behavior. A stochastic simulation model generates stochastic outputs at the same input. Given a budget constraint on total simulation replications, we develop a new approach, which we call stochastic importance sampling, which efficiently uses stochastic simulations with unknown output distribution. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of an estimator. Application to a computationally intensive aeroelastic wind turbine simulation demonstrates the benefits of the proposed approach. Supplementary materials for this article are available online.