  We present a novel way of accelerating hybrid surrogate methods for the
calculation of failure probabilities. The main idea is to use mesh refinement
in order to obtain improved local surrogates of low computation cost to
simulate on. These improved surrogates can reduce significantly the required
number of evaluations of the exact model (which is the usual bottleneck of
failure probability calculations). Meanwhile the effort on evaluations of
surrogates is dramatically reduced by utilizing low order local surrogates.
Numerical results of the application of the proposed approach in several
examples of increasing complexity show the robustness, versatility and gain in
efficiency of the method.
