Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach

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• 作者：Ian J. Davies ^{i.davies@curtin.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Weibull ; Extreme value distribution ; Unbiased estimation ; Weibull modulus ; Linear least squares
• 刊名：Journal of the European Ceramic Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：37
• 期：1
• 页码：369-380
• 全文大小：4395 K

文摘

The wide applicability of the Weibull distribution to fields such as hydrology and materials science has led to a large number of probability estimators being proposed, in particular for the widely used technique of obtaining the Weibull modulus, m, using unweighted linear least squares (LLS) analysis. In this work a systematic approach using the Monte Carlo method has been taken to determining the optimal probability estimators for unbiased estimation of m   (mean, median and mode) using the general equation db5566e5f2632f77c0471feeb14a" title="Click to view the MathML source">F=(i−a)/(N+b)$F=\left(i-a\right)/\left(N+b\right)$ whilst simultaneously minimising the coefficient of variation for each of the average values. A wide range of a and b   values were investigated within the region 0≤a≤1$0\le a\le 1$ and dbb92ed1e23fd26ebc24c4d" title="Click to view the MathML source">1≤b≤1000$1\le \text{b}\le 1000$ with the form of F=(i−a)/(N+1)$F=\left(i-a\right)/\left(N+1\right)$ being chosen as the recommend probability estimator equation due to its simplicity and relatively small coefficient of variation. Values of a as a function of N were presented for the mean, median and mode m values.