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The definition of the relationship between probability, fatigue stress and cycles to failure is of great importance, especially in applications which requires very low probability of failure (e.g. Pf=0.1%). In this paper a new formulation is presented, which allows to separately consider the probability of the endurance and the probability of existence of the initiating defect. This approach is then compared to a number of known models. For this purpose, the proprietary results of 8 fatigue test sets, each with at least 24 data points, have been analyzed. A ranking of goodness-of-fit based on the Relative Likelihood can be used to choose the best distribution within each model, but unfortunately cannot be used to compare different models. The conclusions were: 1- the better description of the HCF strength, in terms of performance and robustness, were obtained by the 2-p Weibull distribution; 2- the choice of the model has a great influence in the estimate of the low probability quantiles, but it still subjective and a definitive answer cannot be given after this benchmark; 3- the strength of the proposed model is its flexibility

Bi-conditional probabilistic fatigue stress-based curve definition and comparison with other models