To investigate fuzzy reliability problem deeply, the traditional failure possibility of the structures with fuzzy variables is explained from the probability perspective. By treating the membership levels of all fuzzy variables as the same random variable following standard uniform distribution, it is verified in theory that the failure probability where the membership levels follow the same standard uniform distribution equals to the traditional failure possibility. Furthermore, by treating the membership levels of the different fuzzy variables as the independent standard uniform distributions, a novel fuzzy reliability model is proposed to measure the safety of the structures with fuzzy variables, which provides a new perspective to analyze the failure mechanism of the structures with fuzzy variables. Comparing the principles and results of the examples with the traditional failure possibility, the proposed model based on the probability perspective utilizes available information more adequately and the results are much closer to the engineering practices, while the traditional approach is too conservative. Moreover, according to the feature of the established fuzzy reliability model, a highly efficient solution based on the kriging surrogate model method is proposed to analyze the reliability of the structure with fuzzy variables. © 2015 Elsevier Ltd.