Application of Lambda Distributions and Bootstrap analysis to the prediction of fatigue lifetime and confidence intervals

Dealing with fatigue lifetime prediction, this paper aims to report on a new statistical method combining the Lambda Distributions and the Bootstrap technique. This method is first applied for determining the Probability Density Function (PDF) of the C and n coefficients in the Paris relationship of a fatigue crack propagation curve. Then, introducing the initial crack's length distribution, the fatigue lifetime prediction is obtained and discussed considering various standard deviations of the initial crack's length. It is shown that the scattering of the initial crack's length needs to be taken into account in predicting lifetime, and that the stochastic nature of the crack's propagation is not self-sufficient to explain completely the experimental asymmetry of the PDF lifetime. This paper shows that the Lambda Distributions are a powerful tool for modelling the PDF lifetime, compared with traditional Gaussian or lognormal PDF.