Predicting reliability levels for critical details of bridges based on limited statistical traffic data is a relevant topic nowadays. That is why the comparison between results from various statistical approaches based on the recorded data for applied traffic actions is the main point of interest of this work. The object of the current study is the famous Millau viaduct, a cable-stayed bridge with the steel orthotropic deck located in Southern France. Values of load effects that are used in analysis are derived from a finite element model of a part of the deck. They are based on data from traffic monitoring that is provided from the bridge Weigh-In-Motion system covering several months of axle loads, distances and speeds of heavy trucks. The methodology is based on a definition of limit state functions based on several statistical distributions in order to assess and compare reliability indexes for the ultimate limit state. It includes a comparison between different approaches of extreme values theory, the methodology proposed in background works for European standards and the design load model. Moreover, this work covers the influence of applied loads of a high amplitude, as global effects, onto stresses from axle loads, as local effects.