The fatigue-limit model studied here contains an unknown fatigue limit parameter. Under this model, specimens tested below this fatigue-limit level of stress will never fail. The model also allows the standard deviation of fatigue life to be a function of stress. Researchers can use this model to describe the standard deviation and stress dependence in fatigue data. To illustrate its application, we use maximum likelihood methods to fit the model to fatigue data on a nickel base superalloy. Modern statistical methods based on likelihood ratio provides confidence intervals for the fatigue limit parameter. We also study the effect that test length has on estimation by analyzing simulated data sets based on this model. Through this simulation study, we gain insight on practical test lengths for future fatigue experiments.