Unbiased weighted least squares estimation of Weibull modulus with small samples

Weibull distribution has been used vastly for modeling the fracture strength of ceramic and composite materials.Estimating the Weibull modulus is an important problem, particularly in cases where the sample size is small due to high experimental costs.The Ordinary Least Squares (OLS) method is the most commonly used method by materials scientists.Numerous probability estimators have been proposed using the OLS method, and most of these studies focused on unbiased estimation.Weighted Least Squares (WLS) is a promising alternative to OLS, yet, there are only a few studies on this subject.This work followed a systematic analysis to develop a new probability index for unbiased estimation of Weibull modulus using WLS.For sample sizes less than 60, the performance of the new index is shown to be significantly superior to currently used OLS methods and is better or as good as the Maximum Likelihood Estimation method.