There are many types of reliability analysis method: linear approximation – first-order reliability method (FORM), and quadratic approximation – second-order reliability method (SORM), and most probable point based dimension reduction method (MPP-based DRM). The reliability analysis using FORM has an advantage in terms of computation efficiency, but the accuracy is not good when the performance function is highly nonlinear and multi-dimensional. In SORM, using the quadratic approximation, the computational accuracy is higher than FORM but the efficiency is lower. The MPP-based DRM, the most recently proposed method, has advantages of the FORM and SORM at the same time in the efficiency and the accuracy. However, the reliability analysis using the MPP-based DRM does not consider the cross-term of the performance function, so that it cannot obtain higher accuracy.
The main objective of this paper is to develop an accurate methodology for the MPP-based DRM by using the subspaces considering cross-term. When using the general bivariate DRM, it is possible to increase the accuracy because many cross-terms can be considerable, but the efficiency becomes lower as the dimension of the performance function increases. For this reason, subspace is applied by considering the important cross-term in the general bivariate DRM, thereby minimizing the efficiency reduction. The accuracy improvement of the probability of failure estimation is demonstrated with several numerical examples.