Reliability analysis for implicit limit state equation

In order to obtain the failure probability of the implicit limit state equation accurately, advanced mean value second order (AMVSO) method was presented, and advanced mean value (AMV) in conjunction with the response surface method (RSM) was also presented. The implementations were constructed on the basis of the advanced mean value first order (AMVFO) method and the RSM. The examples show that the accuracy of the AMVSO is higher than that of the AMVFO. The results of the AMV in conjunction with the RSM are not sensitive to the positions of the sampling points for determining the response surface equation, which illustrates the robustness of the presented method.