Reliability sensitivity analysis based on subset simulation and importance sampling

Reliability sensitivity algorithm is presented on the basis of subset simulation and importance sampling due to the small failure probability highly experienced in engineering. Firstly, a small failure probability is expressed as a product of larger conditional failure probabilities of some intermediate failure events. Secondly, the larger conditional failure probabilities can be estimated efficiently by constructing the importance sampling density functions of the intermediate failure events. Thirdly, the reliability sensitivity is transformed into the partial derivatives of conditional failure probabilities with respect to the distribution parameters of the basic variables in the paper. The estimation of the reliability sensitivity and its variance are then derived for the presented algorithm. The results from several cases show that the present method is efficient, precise and applicable to the structural system with single and multiple failure modes.