Markov chain-based line sampling method for reliability estimation of structural parallel system with multiple failure modes

In order to reduce the variance of the failure probability estimation of a structural parallel system with multiple failure modes, we develop the Markov chain-based line sampling method for its reliability estimation in accordance with the definition of its important direction and the line sampling method for single failure mode. The method uses the Markov chain to simulate the conditional samples in the failure domain of the structural parallel system. The conditional samples are employed both for determining the important direction and for estimating the reliability with the line sampling method, thus greatly reducing the variance of failure probability estimation, as can be concluded from eq. (11) in the full paper. The method combines the calculation of important direction with the failure probability estimation obtainable from the conditional samples and thus fully utilizes the distribution information contained in the conditional samples. Finally, four numerical examples, whose results are given in Tables 1, 2 and 4 in the full paper, show preliminarily that, compared with the traditional Monte Carlo simulation, the sampling efficiency of our method is much higher and its computation load is much smaller.