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This paper deals with the problem of estimating the volume of the excursionset of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold,under a probability measure on $\mathbb{R}^d$ that is assumed to be known. Inthe industrial world, this corresponds to the problem of estimating aprobability of failure of a system. When only an expensive-to-simulate model ofthe system is available, the budget for simulations is usually severely limitedand therefore classical Monte Carlo methods ought to be avoided. One of themain contributions of this article is to derive SUR (stepwise uncertaintyreduction) strategies from a Bayesian-theoretic formulation of the problem ofestimating a probability of failure. These sequential strategies use a Gaussianprocess model of $f$ and aim at performing evaluations of $f$ as efficiently aspossible to infer the value of the probability of failure. We compare thesestrategies to other strategies also based on a Gaussian process model forestimating a probability of failure.

Sequential design of computer experiments for the estimation of a probability of failure