• lognormal distribution;
  • Monte Carlo method;
  • fatigue modelling;
  • probabilistic analysis;
  • SN curve;
  • non-constant standard deviation


Fatigue life reliability often is accounted for through minimal material data. To provide this information within structural calculation, experimental data from specimen testing needs to be processed with statistical methods. The results are either mean or worst case material data. However, in a robust design environment, scatter itself must be numerically available. In this paper, fatigue test results of a nickel-based super alloy at two temperatures are taken from literature. These data are processed according to ASTM standard E739 to identify median and standard deviation, based on a stress life curve (SN curve) in double logarithmic coordinates first proposed by Basquin. In addition, a new method for non-constant standard deviation is applied to the dataset. The SN curve parameters are treated with a statistical distribution to account for scatter in the material data. The basic parameter set is perturbed by Monte Carlo simulation to generate pseudo-scatter in the life result, which can be plotted as a Wöhler field. This pseudo-scatter is analysed and compared to the ASTM constant standard deviation regression. Statistical methods are used to show that a realistic prediction of fatigue life is feasible using the Perturbation approach. Both models represent the literature fatigue data very well, whereas the Perturbation approach provides more flexibility. It is especially recommended for black box Monte Carlo studies of structural lifing. The Perturbation approach is additionally capable of including runouts and using other life curves than such of SN type.