An improved line sampling method and its application based on conditional expectation

In order to reduce the variance in calculating the reliability and sensitivity with the line sampling method, a total variance formula is subtly employed and a conditional expectation is introduced to improve the traditional method. At the same time, the reliability and sensitivity formulae are respectively transformed into a form that is independent of the dimension of the input variables and then solved by the kernel density estimation method, so that solving the conditional expectation with demanding computation is avoided. The proposed method is applied to some engineering examples with MATLAB software, and the results all show that the improvement in the traditional line sampling method has made an obvious contribution to the convergency and stability of the failure probability and sensitivity.