Abstract: Three improved methods are proposed for the measurements of probabilistic fatigue limits under the fatigue tests of up-and-down method. It is revealed that the convention- al method for the measurements couldn’t reasonably reflect the stochastic feature of the limits, and exists inevitably errors of measurements. The improved methods, by the three possible cases of given test data, are constructed by the so-called “random localized Basquin S-N relations” in the range of around the limits. The randomness for the limits is represented by the fatigue lives related to the local relations. Availabilities of the improved methods are indicated by the estimations of the probabilistic fatigue limits of LZ50 axle steel for the Chinese railway vehicles.

Key words: Fatigue limit, LZ50 steel, Probabilistic analyses