Statistical distributions for the size of fatigue-initiating defects in Al–7%Si–0.3%Mg alloy castings: A comparative study

Statistical distributions used in the literature for size distributions of fatigue-initiating defects are reviewed. Seven distributions from the literature are fitted to two datasets for the fatigue-initiating defects in A356 aluminum alloy castings, reported previously by Yi et al. [J.Z. Yi, P.D. Lee, T.C. Lindley, T. Fukui, Mater. Sci. Eng. A, A432 (2006) 59]. The results of the goodness-of-fit tests indicate that only lognormal, Gumbel and General Extreme Value distributions provide acceptable fits to both datasets. Weibull, Fréchet and Generalized Pareto distributions do not provide good fits to the two datasets. Based on mathematical statistics, however, it is recommended that only Gumbel or General Extreme Value distributions be used for the size of fatigue-initiating defects. The effect of using the correct statistical distribution for the size of defects on the accuracy of the fatigue life estimates is demonstrated.