The Importance Sampling method is a type of reliability method where a distribution other than the original distribution is used to compute the probability of failure more efficiently (Southwest Research Institute, 1998).
Importance Sampling, like the First Order Reliability Method (FORM), computes the most Probable Point (MPP)—the point on the constraint that is closest to the mean value point in the standard normal space. A transformation is used to map the original random vector X (in X-space) to the standard, uncorrelated normal vector using U = T(X).