The moving particles method for reliability estimation: recent advances

In the following, recent advances of the moving particles method are highlighted. A multi level version of the estimator is introduced that balances the statistical error and the numerical approximation error by computing a telescoping sum of estimates for the number of moves. An extension to general model classes in the sense of a multi fidelity method is obtained based on the estimation of bivariate Poisson distributions for censored data. Finally, the local sensitivity of the reliability estimate with respect to the parameters of the probability characteristics of the model input is considered. It is shown how to obtain estimates of the local sensitivity without any additional function evaluations.