System reliability analysis with saddlepoint approximation

System reliability is usually estimated through component reliability, which is commonly computed by the First Order Reliability Method (FORM). The FORM is computationally efficient, but may not be accurate for nonlinear limit-state functions. An alternative system reliability analysis method is proposed based on saddlepoint approximation. Unlike the FORM that linearizes limit-state functions in a transformed random space, the proposed method linearizes the limited-state functions without any transformation. After the linearization, the joint probability density of limit-state functions is estimated by the multivariate saddlepoint approximation. Without the nonnormal-to-normal transformation, the present method is more accurate than the FORM when the transformation increases the nonlinearity of limit-state functions. As demonstrated in the two examples, the new method is also as efficient as the FORM.