On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions

Many systems have multiple failure modes that result in multiple performance functions. In this paper, a new stochastic simulation based approach is proposed for evaluation of multiple failure probability curves in a reliability problem with multiple performance functions. The state-of-the-art stochastic simulation based techniques, such as subset simulation and auxiliary domain method, are efficient in evaluating a failure probability curve but only consider a single performance function. Standard Monte Carlo simulation is robust to the type and dimension of the problem and is applicable to evaluate multiple failure probability curves for a problem with multiple performance functions but is computationally expensive especially while estimating small probabilities. The proposed approach for simultaneous consideration of multiple performance functions generalizes the subset simulation and is an improvement of the generalized subset simulation. The output of an analysis using the proposed approach is multiple failure probability curves with each corresponding to one performance function. The proposed approach is robust with respect to the dimension of the failure probability integral, model complexity, the degree of nonlinearity, number of performance functions, and efficient in cases involving the computation of small failure probabilities. The effectiveness and efficiency of the proposed approach are demonstrated by three numerical examples.