New sampling method and procedures for estimating failure probability

A new sampling method on the basis of a distance index and spherical subset simulation is proposed in this paper, with which the samples of uncertain variables are equally generated in the possible domain of uncertain variables and the failure probability is estimated using the concept of conditional probability. Coupling with this new sampling method, two practical procedures are developed for estimating the failure probability: one is a coarse procedure for the analysis of ordinary problems and the other is a refined procedure for the analysis of critical problems. The accuracy and efficiency of the proposed sampling method and procedures for estimating the failure probability are demonstrated through a series of examples. The results show that the proposed approach is valid for general applications and can yield an accurate estimate of the failure probability. The accuracy and efficiency are not influenced by the distribution type of uncertain variables, correlation among uncertain variables, nonlinearity of the performance function, and dimension of uncertain variables.