dc.contributor.author Davies, Ian dc.date.accessioned 2017-11-24T05:24:25Z dc.date.available 2017-11-24T05:24:25Z dc.date.created 2017-11-24T04:48:49Z dc.date.issued 2017 dc.identifier.citation Davies, I. 2017. Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach. Journal of European Ceramic Society. 37 (1): pp. 369-380. dc.identifier.uri http://hdl.handle.net/20.500.11937/58201 dc.identifier.doi 10.1016/j.jeurceramsoc.2016.07.008 dc.description.abstract © 2016 Elsevier Ltd 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 F=(i-a)/(N+b) 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 and 1=b=1000 with the form of F=(i-a)/(N+1) 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. dc.publisher Elsevier Ltd dc.title Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach dc.type Journal Article dcterms.source.volume 37 dcterms.source.number 1 dcterms.source.startPage 369 dcterms.source.endPage 380 dcterms.source.issn 0955-2219 dcterms.source.title Journal of European Ceramic Society curtin.department Department of Mechanical Engineering curtin.accessStatus Fulltext not available
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