First-order saddlepoint approximation for reliability analysis

In the approximation methods of reliability analysis, nonnormal random variables are transformed into equivalent standard normal random variables. This transformation tends to increase the nonlinearity of a limit-state function and, hence, results in less accurate reliability approximation. The first-order saddlepoint approximation for reliability analysis is proposed to improve the accuracy of reliability analysis. By the approximation of a limit-state function at the most likelihood point in the original random space and employment of the accurate saddlepoint approximation, the proposed method reduces the chance of an increase in the nonlinearity of the limit-state function. This approach generates more accurate reliability approximation than the first-order reliability method without an increase in the computational effort. The effectiveness of the proposed method is demonstrated with two examples and is compared with the first- and second-order reliability methods.