Analysis of Estimation of Parameters in 3P-Weibull KJc Distribution: Sample Size Effect

Abstract

The minimum sample size for a good estimation of the parameters in both three-parameter Weibull KJc distribution (3P-W) and ASTM E1921 methods was analyzed. Additionally, the estimations provided by maximum likelihood (ML) and linear regression (LR) were compared. Fracture toughness sets with different sample sizes were randomly generated following a 3P-W with parameters corresponding to experimental datasets from the Euro round robin fracture toughness test. Then, LR and ML were applied to the sets and the parameters were estimated. Standard deviation (SD) and interquartile range (IQR) were employed to analyze the goodness of fit. The results of this paper were consistent with the necessity of large sample sizes (over 30) to find a representative value of the threshold and shape parameters. However, the scale parameter showed a lower scatter and can be estimated with a smaller sample size (around six samples), as used in the standard ASTM E1921-19b.