A statistical fatigue model to predict the Wöhler field for any combination of σ_min, σ_max or R = σ_min / σ_max is presented. The model extends an existing model to the case of σ_max being tension and σ_min being tension or compression, and is derived based on physical, statistical and compatibility conditions, thus, eliminating the selection of arbitrary functions. The main tool to derive the model is a functional equation, which allows obtaining the most general model satisfying all the stated conditions. In particular, the regression formula for the σ_max-log N field for fixed R values is analyzed. A particular and powerful model is selected and its main properties are derived. This model is applied to some real data to illustrate its applicability to practical problems. The results seem to be very promising, especially because the model, due to its physical and statistical constraints, appears to be very robust and with a high capacity to detect outliers.