Subset Simulation – A New Approach to Calculating Small Failure Probabilities

A new simulation approach, called 'subset simulation', is proposed to compute small failure probabilities. The basic idea is to express the failure probability as a product of larger conditional failure probabilities by introducing intermediate failure events. With a proper choice of the intermediate failure events, the original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which are efficiently estimated by simulation using a special Markov chain. The proposed method is robust to the number of uncertain parameters and efficient in computing small probabilities. An example of calculating the first-excursion probability of a five-story shear building under uncertain seismic excitation is presented to demonstrate the efficiency of the method.