Analysis of the fatigue life estimators of the materials using small samples

Abstract

Knowledge of the stochastic nature of fatigue life of composite materials can be modeled by the failure time with the Weibull distribution. This task becomes complex when the samples are small and scattered. In this way, it is necessary to know and to improve robust models of estimation of the parameters of the distribution of Weibull. The aim of this work is to compare the performance of least squares, least squares weighted, maximum likelihood estimator and momentum method and to suggest a method that obtains better performance in life behavior to fatigue with small samples. Monte Carlo simulations were performed to estimate the distribution parameters with different sample sizes and an application with real fatigue data that compares performance using goodness-of-fit. The results of the simulations showed that the weighted least squares estimation was able to generate more reliable estimators for fatigue behavior during its useful life. In this way, it is possible to conclude that small samples make the real representation of life difficult to the material fatigue, but using the weighted least squares estimation method, it is possible to obtain more estimates.