Effect of Scatter Direction on the Maximum Likelihood Evaluation of Bilinear S-N Curves

The statistical evaluation of S-N curves plays a central role in fatigue analysis, especially under the constraint of limited test data and the presence of runouts. While traditional approaches focus on modeling uncertainty in the fatigue-life direction, this study investigates four different evaluation strategies for the bilinear Basquin model using maximum likelihood estimation: (1) minimization in the fatigue-life direction, (2) minimization in the load direction, (3) a hybrid piecewise transformation approach, and (4) a novel hybrid pointwise transformation approach. All models are formulated within a consistent probabilistic framework based on a log-normal distribution. A systematic Monte Carlo study examines the performance of these strategies under variation of key parameters such as the number of data points, the logarithmic standard deviation, and the runout ratio. The results show that the commonly used evaluation in the fatigue-life direction yields the poorest parameter estimates. The load-based evaluation performs well in estimating the load amplitude at the knee point and the corresponding fatigue life, but struggles with slope accuracy due to truncation effects. The newly introduced pointwise transformation and the piecewise transformation improve robustness for higher runout ratios. Overall, load-based evaluation performs best at low runout ratios, whereas piecewise and pointwise evaluations outperform under higher censoring. These findings contribute to a better understanding of the directional assumptions in statistical S-N modeling and support the development of more reliable fatigue assessment methods.