Saddlepoint approximation and Nataf transformation based total effect analysis of basic variable in multiple failure modes

For reliability model with multiple failure modes commonly used in practical engineering, the saddlepoint approximation method is employed to analyze the total effect of the basic random variable in case of the multiple failure modes. In the proposed method, saddlepoint approximation method is combined with Nataf transformation for approximating the unconditional joint probability density function and conditional joint one of the multiple response performance function, on which the total effect of the basic random variable on the probability distribution of the multiple response performance function can be calculated. The concept and the implementation of the proposed method are described step by step, and several examples are used to verify the rationality and feasibility of proposed method.