  Assume that a Gaussian process $\xi$ is predicted from $n$ pointwise
observations by intrinsic Kriging and that the volume of the excursion set of
$\xi$ above a given threshold $u$ is approximated by the volume of the
predictor. The first part of this paper gives a bound on the convergence rate
of the approximated volume. The second part describes an algorithm that
constructs a sequence of points to yield a fast convergence of the
approximation. The estimation of the volume of an excursion set is a highly
relevant problem for the industrial world since it corresponds to the
estimation of the failure probability of a system that is known only through
sampled observations.
