Estimation of probability of failure using bootstrap methods

For modelling under uncertainty, Monte-Carlo Simulations is the most popular way of propagating the uncertainty from input parameters to outputs. However, any reliability index, such as probability of failure, based on sampling methods is subject to variability. This variability can lead to underestimations/overestimations, so it is always beneficial to find methods that can provide estimates with confidence levels. Bootstrap methods can address these two issues and allow us to evaluate the uncertainty of our estimates and to use this information to generate conservative estimators of reliability. A simple numerical example is used to illustrate the method and target probability on the accuracy of such estimates.