Structural reliability methods aim at computing the probability of failure ofsystems with respect to some prescribed performance functions. In modernengineering such functions usually resort to running an expensive-to-evaluatecomputational model (e.g. a finite element model). In this respect simulationmethods, which may require $10^{3-6}$ runs cannot be used directly. Surrogatemodels such as quadratic response surfaces, polynomial chaos expansions orkriging (which are built from a limited number of runs of the original model)are then introduced as a substitute of the original model to cope with thecomputational cost. In practice it is almost impossible to quantify the errormade by this substitution though. In this paper we propose to use a krigingsurrogate of the performance function as a means to build a quasi-optimalimportance sampling density. The probability of failure is eventually obtainedas the product of an augmented probability computed by substituting themeta-model for the original performance function and a correction term whichensures that there is no bias in the estimation even if the meta-model is notfully accurate. The approach is applied to analytical and finite elementreliability problems and proves efficient up to 100 random variables.
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