Buckling Restrained Braces (BRBs) play an essential role in seismic protection due to their remarkable energy dissipation capacity, ductility, and stiffness. This paper represents the first thorough evaluation of the reliability and uncertainty of BRBs, accounting for various sources of uncertainty and varied conditions, such as different gap sizes, friction coefficients between the encasing and the steel core, and other geometric and mechanical properties of the connecting parts. This paper introduces an innovative application of an integrated probabilistic approach that combined Finite Element (FE) modeling, Artificial Neural Networks (ANN), and Monte Carlo simulation to characterize the seismic behavior of BRBs. Experimental results from literature is used to validate the FE model constructed using ABAQUS. This validated model is then integrated into a Low-rank Tensor Approximation process to yield variance-based sensitivity measures for the considered variables. The most influential variables identified in this process along with the calibrated FE model is utilized to conduct a reliability assessment through an ANN-assisted Monte Carlo simulation. This analysis is conducted to quantify the reliability level of the investigated BRBs as a function of the gap size and establish the resistance factors necessary to maintain the reliability level above prescribed thresholds. It was found that the highest reliability can be achieved at a small gap size equal to half the radius of gyration of the main steel core, requiring a resistance factor of 0.9. For gap sizes higher than this value, a resistance factor ranging between 0.70 and 0.85 is needed.