Reliability analysis provides a logical methodology for the estimation of the probability of failure of a system and often requires many runs of an expensive-to-evaluate limit state function. Surrogate models can be deployed to reduce the computational cost associated with such analysis, Kriging being arguably the best-known surrogate model for reliability analysis. Although replacing full-scale simulations with surrogate models is well-established for deterministic limit state functions, there is still the need to extend it to non-deterministic cases. To bridge this gap, we propose using regression-based surrogate models for reliability estimation of noisy limit state functions. The performance of this method is demonstrated on well-known reliability benchmark problems artificially corrupted with noise. Our results show that regression-based surrogate models can be used to effectively denoise these models and estimate the associated probability of failure.