A sequential Bayesian algorithm to estimate a probability of failure

This paper deals with the problem of estimating the probability of failure of a system, in the challenging case where only an expensive-to-simulate model is available. In this context, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. We present a new strategy to address this problem, in the framework of sequential Bayesian planning. The method uses kriging to compute an approximation of the probability of failure, and selects the next simulation to be conducted so as to reduce the mean square error of estimation. By way of illustration, we estimate the probability of failure of a control strategy in the presence of uncertainty about the parameters of the plant.