A subset simulation method based on conditional expectation

In order to reduce the variance in estimating the probability failure and reliability sensitivity, an improved subset simulation method is put forward. The proposed method is based on total variance formula in which the variance of the multidimensional variables with conditional expectation is not greater than that of the variables themselves. So that the mean of multidimensional variables to estimate the probability failure and reliability sensitivity is transformed into the mean of conditional expectation in this paper. The latter contains twofold probability estimation and then is converted into an integral form that can be estimated with kernel density to reduce the variance without calculation increasing. Finally, some examples demonstrate that the theoretical analysis is correct and the proposed method reduces the variance and improves the convergence and stability in calculating the probability failure and reliability effectively.