<p>The fatigue of heavy-haul railway bridges is considered a key concern due to high stress levels and cyclic loading. The evaluation of fatigue reliability is required to include factor correlations. A major challenge is presented by the construction of the cumulative distribution function (CDF) and the description of correlations between random variables. In this study, the copula function is used to analyze the fatigue failure probability of the Shuohuang heavy-haul railway bridge. A C-vine copula (CVC)-based joint probability density function (JPDF) is derived with eight correlated parameters. To enhance efficiency in small failure probability calculations, the subset simulation and most probable point (MPP) Monte Carlo importance sampling are introduced based on the Rosenblatt transform and C-vine model. Comparisons with traditional Monte Carlo methods confirm that high accuracy and efficiency are achieved. The results show that when parameter correlations are ignored, failure probability is underestimated, increasing safety risks in bridge assessments.</p>