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

    Access Status
    Fulltext not available
    Authors
    Davies, Ian
    Date
    2017
    Type
    Journal Article
    
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    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.
    Source Title
    Journal of European Ceramic Society
    DOI
    10.1016/j.jeurceramsoc.2016.07.008
    ISSN
    0955-2219
    School
    Department of Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/58201
    Collection
    • Curtin Research Publications
    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.

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