In the sixties last century started the story of failure probability estimation methods in structural reliability. In the beginning there were two approaches: to find suitable importance sampling methods to one and the second to approximate the failure domain by domains with a simpler structure, i.e. a with a linear or quadratic limit state function (LSF). Essential here is the structure of the LSF near the design points.
In the eighties and nineties is was found that by studying the behavior of the LSF near the design points one can derive parameter sensitivities. In the noughties then as it became clear that the FORM/SORM methods become increasingly inefficient for high-dimensional problems, the research interest shifted to refined MC methods. However by this move the geometrical understanding of the original problem was lost.
Using asymptotic analysis one can show that all these new methods subset simulation, line sampling and cross entropy methods end up doing MC sampling near the design points. So one gets to back the geometrical structure. From this findings one can see that it is possible to improve the analytic approximation methods by suitable MC importance sampling methods. The conclusion is that the best way for failure probability estimation is to start from the design points and to make some sort of importance sampling around these. So one avoids the time consuming and error prone iterative procedures in the newer schemes which end up at the design points anyway and by additional MC sampling around them one gets efficient estimates for probabilities and sensitivities also for high-dimensional problems.