The primary objective of this research is to develop a new stochastic method, referred to as High Dimensional Model Representation (HDMR) based response surface, for general reliability analysis of complex engineering systems. The current effort involves: (1) development of an efficient approximate method for reliability analysis involving the limit state/performance function which is dominantly of additive or multiplicative in nature, (2) development of multipoint response surface for reliability analysis, involving multiple design points, (3) formulation of generalized response surface techniques for probabilistic characterization of general class of problems, and (4) development of convolution theorem based approach for reliability analysis in conjunction with HDMR based response surface modeling. The convolution integral is solved efficiently using the Fast Fourier Transform (FFT), and the limit state/performance function is approximated using HDMR at the most probable point.

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