An improved reliability index based on regional equivalent conversion

Aiming at the accuracy and efficiency of traditional reliability method for solving highly nonlinear problem, this paper proposes the regional equivalent conversion index (RECI) to compute reliability under arbitrary boundary and number of subdomains of limit state function. Firstly, we establish the model of RECI and the corresponding sampling method. Furthermore, the RECI of a series of parallel linear performance functions are computed by the proposed method. Besides the advanced first order and second moment method (AFOSM) are used to compute the reliability. Finally, the mapping relationship between RECI and reliability is established. Influence of sampling parameters on relative error is studied and optimal value is given. The parameters are optimized by analyzing the influence of the parameters on the precision. This method is also suitable for multiple failure modes without changing any process. Numerical examples are employed to demonstrate the feasibility of the proposed method for solving highly nonlinear problem in dimension 1–4.