Some advances in importance sampling of reliability models based on zero variance approximation

We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results.