An adaptive subset simulation algorithm for system reliability analysis with discontinuous limit states

Many system reliability problems involve performance functions with a discontinuous distribution. Such situations occur in both connectivity- and flow-based network reliability problems, due to binary or multi-state random variables entering the definition of the system performance or due to the discontinuous nature of the system model. When solving this kind of problems, the standard subset simulation algorithm with fixed intermediate conditional probability and fixed number of samples per level can lead to substantial errors, since the discontinuity of the output can result in an ambiguous definition of the sought percentile of the samples and, hence, of the intermediate domains. In this paper, we propose an adaptive subset simulation algorithm to determine the reliability of systems whose performance function is a discontinuous random variable. The proposed algorithm chooses the number of samples and the intermediate conditional probabilities adaptively. We discuss two MCMC algorithms for generation of the samples in the intermediate domains, the adaptive conditional sampling method and a novel independent Metropolis–Hastings algorithm that efficiently samples in discrete input spaces. The accuracy and efficiency of the proposed algorithm are demonstrated by a set of numerical examples.