caa a22 4500 463227913 CHVBK 20180405153232.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10853-007-2060-5 doi (NATIONALLICENCE)springer-10.1007/s10853-007-2060-5 On estimating Weibull modulus by the linear regression method [Elektronische Daten] [Murat Tiryakioğlu, David Hudak] Statistical models were developed to estimate the bias of the shape parameter of a 2-parameter Weibull distribution where the shape parameter was estimated using a linear regression. These models were formulated for 27 sample sizes from 5 to 100 and for 35 probability estimators, $$ P = {(i - a)} \mathord{\left/ {\vphantom {{i - a} {n + b}}} \right. \kern-\nulldelimiterspace} {(n + b)} $$ , by varying "a” and "b”. In each simulation, 20,000 trials were used. From these models, a class of unbiased estimators were developed for each sample size. The standard deviation and coefficient of variation of these estimators were compared to the bias of the estimators. The standard deviation increased while the coefficient of variation decreased with increasing bias of the shape parameter. Also, the Anderson-Darling statistics was used to determine that the normal, log-normal, 3-parameter Weibull, and 3-parameter log-Weibull distributions did not provide good fit to the estimator of the shape parameter. Springer Science+Business Media, LLC, 2007 Tiryakioğlu Murat Department of Engineering, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, 15108, Moon Township, PA, USA aut Hudak David Department of Mathematics, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, 15108, Moon Township, PA, USA aut Journal of Materials Science Springer US; http://www.springer-ny.com 42/24(2007-12-01), 10173-10179 0022-2461 42:24<10173 2007 42 10853 https://doi.org/10.1007/s10853-007-2060-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10853-007-2060-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tiryakioğlu Murat Department of Engineering, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, 15108, Moon Township, PA, USA aut NATIONALLICENCE 700 1- Hudak David Department of Mathematics, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, 15108, Moon Township, PA, USA aut NATIONALLICENCE 773 0- Journal of Materials Science Springer US; http://www.springer-ny.com 42/24(2007-12-01), 10173-10179 0022-2461 42:24<10173 2007 42 10853 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer