Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach
© 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...
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| Format: | Journal Article |
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Elsevier Ltd
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/58201 |
| _version_ | 1848760201157541888 |
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| author | Davies, Ian |
| author_facet | Davies, Ian |
| author_sort | Davies, Ian |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 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. |
| first_indexed | 2025-11-14T10:12:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-58201 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:12:00Z |
| publishDate | 2017 |
| publisher | Elsevier Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-582012017-11-24T05:46:22Z Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach Davies, Ian © 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. 2017 Journal Article http://hdl.handle.net/20.500.11937/58201 10.1016/j.jeurceramsoc.2016.07.008 Elsevier Ltd restricted |
| spellingShingle | Davies, Ian Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title | Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title_full | Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title_fullStr | Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title_full_unstemmed | Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title_short | Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach |
| title_sort | unbiased estimation of weibull modulus using linear least squares analysis—a systematic approach |
| url | http://hdl.handle.net/20.500.11937/58201 |