Separable Monte Carlo combined with importance sampling for variance reduction

Monte Carlo (MC) methods are often used to carry out reliability based design of structures. Methods that improve the accuracy of MC simulation include Separable Monte Carlo (Separable MC), Markov Chain Monte Carlo and importance sampling. We explore the utility of combining Separable MC and importance sampling for improving accuracy. The accuracy of the estimates is compared for Standard MC, Separable MC, importance sampling and combined method for a composite plate example and a tuned mass damper example. For these examples Separable MC and importance sampling reduced the error individually by factors of 2‐5, and the combination reduced it further by about a factor of 2. The results were also compared with the First Order Reliability Method (FORM). FORM was grossly inaccurate for the tuned mass‐damper example which has a failure region bounded by safe regions on either side.