This paper is concerned with an importance sampling method combined with the conditional expectation in simulation-based structural reliability assessment. First, approximated optimal importance sampling marginal densities are determined by using the result of a piecewise integral of the failure probability. Next, an importance sampling simulation with a small number of sample sizes is executed by using importance sampling densities above determined and then the importance sampling region is roughly identified. The piecewise integral of the failure probability is executed again over the restricted importance sampling region, and the result of failure probability is used to reconstruct the approximated optimal importance sampling marginal densities. The same procedure is repeated and the structural failure probability is estimated through the importance sampling simulation. The procedure is referred to as a repeated importance sampling. Numerical example is provided to demonstrate the validity of the proposed method. The proposed method gives the accuracy of failure probability with shorter processing time.
