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• In reliability disintegration, computing reliability index is still a challenge. In this research a impressive reliability algorithm is proposed. • The algorithm is a combination of the particle swarm optimization (PSO) and differential evolution (DE) algorithms. • The proposed algorithm (DEPSO) is implemented in ten numerical nonlinear examples. • This proposed algorithm is much easier than other optimization schemes. • Results illustrate that the proposed algorithm is effective and as simple as the several other methods but more robust and accurate. The accurate estimation of the health (reliability) index is important to estimate probability of failure in the reliability assessment of structures. The conventional first-order reliability methods including the Hasofer-Lind, Rackwitz-Fiessler, and Monte Carlo could lead to unstable, fluctuating, and distorted solutions to nonlinear problems, featuring complicated structural performance functions. The present study aimed to propose a new method by combining the particle swarm optimization and differential evolution algorithms in order to calculate the reliability index. The performance of the proposed method was evaluated by 10 examples from different studies, and the convergence results were compared to the results of studies such as Hasofer-Lind, Rackwitz-Fiessler, Monte Carlo and some other methods. To verify the accuracy of the proposed method, to verify the accuracy of the proposed method, a reliability index chart was applied. The comparisons indicated the high accuracy and speed of the proposed method. Accordingly, in higher order nonlinear problems, the proposed method successfully calculated the reliability index while some failed to solve these problems. [ABSTRACT FROM AUTHOR]