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

Q2 Engineering

Engineering Transactions Pub Date : 2021-06-09 DOI:10.24423/ENGTRANS.1172.20210607

Diego Omar Alias, J. E. Ipiña, C. Berejnoi

引用次数: 0

Abstract

The minimum sample size for a good estimation of the parameters in both three-parameter Weibull K Jc 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 E1921-19 b .

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3P威布尔KJc分布参数估计的分析：样本量效应

分析了在三参数威布尔KJc分布（3P-W）和ASTM E1921方法中用于良好估计参数的最小样本量。此外，还比较了最大似然（ML）和线性回归（LR）提供的估计。根据3P-W随机生成具有不同样本量的断裂韧性集，其参数与欧洲循环断裂韧性测试的实验数据集相对应。然后，将LR和ML应用于集合并估计参数。采用标准差（SD）和四分位间距（IQR）分析拟合优度。本文的结果与大样本量（超过30）的必要性相一致，以找到阈值和形状参数的代表值。然而，标度参数显示出较低的散射，并且可以用较小的样本量（大约六个样本）来估计，如标准ASTM E1921-19 b中所使用的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering Transactions Engineering-Engineering (all)

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Engineering Transactions (formerly Rozprawy Inżynierskie) is a refereed international journal founded in 1952. The journal promotes research and practice in engineering science and provides a forum for interdisciplinary publications combining mechanics with: Material science, Mechatronics, Biomechanics and Biotechnologies, Environmental science, Photonics, Information technologies, Other engineering applications. The journal publishes original papers covering a broad area of research activities including: experimental and hybrid techniques, analytical and numerical approaches. Review articles and special issues are also welcome. Following long tradition, all articles are peer reviewed and our expert referees ensure that the papers accepted for publication comply with high scientific standards. Engineering Transactions is a quarterly journal intended to be interesting and useful for the researchers and practitioners in academic and industrial communities.