## Sequential design of computer experiments for the estimation of a probability of failure.(English)Zbl 1252.62081

Summary: This paper deals with the problem of estimating the volume of the excursion set 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. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of f and aim at performing evaluations of f as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.

### MSC:

 62L05 Sequential statistical design 62M09 Non-Markovian processes: estimation 62N05 Reliability and life testing 62F15 Bayesian inference 65C05 Monte Carlo methods

KrigInv; EGO
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### References:

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