Confidence limits for Weibull parameters estimated using linear least squares analysis
© 2017 Elsevier Ltd Confidence limits (at selected levels of 68.27%, 90%, 95% and 99%) for unbiased estimation of Weibull parameters obtained using linear least squares (LLS) analysis were investigated in this paper. A Monte Carlo procedure was used to obtain probability distributions for unbiased e...
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| Format: | Journal Article |
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Elsevier Ltd
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/58210 |
| _version_ | 1848760203899568128 |
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| author | Davies, Ian |
| author_facet | Davies, Ian |
| author_sort | Davies, Ian |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017 Elsevier Ltd Confidence limits (at selected levels of 68.27%, 90%, 95% and 99%) for unbiased estimation of Weibull parameters obtained using linear least squares (LLS) analysis were investigated in this paper. A Monte Carlo procedure was used to obtain probability distributions for unbiased estimates of Weibull modulus, m, and Weibull scale parameter, S o , as a function of total specimen number, N (10 = N = 200), and m (1 = m = 25). Inspection of the probability distributions indicated that confidence limits for m depended only on N whereas those for S o depended on both N and m. Whilst the determination of confidence limits for m proved to be relatively straightforward, the respective values for S o were obtained by fitting an empirical equation to the S o probability distributions approximated by a Gaussian curve. Example values of m and S o confidence limits for selected N have been presented in this work. |
| first_indexed | 2025-11-14T10:12:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-58210 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:12:03Z |
| publishDate | 2017 |
| publisher | Elsevier Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-582102017-11-24T05:46:18Z Confidence limits for Weibull parameters estimated using linear least squares analysis Davies, Ian © 2017 Elsevier Ltd Confidence limits (at selected levels of 68.27%, 90%, 95% and 99%) for unbiased estimation of Weibull parameters obtained using linear least squares (LLS) analysis were investigated in this paper. A Monte Carlo procedure was used to obtain probability distributions for unbiased estimates of Weibull modulus, m, and Weibull scale parameter, S o , as a function of total specimen number, N (10 = N = 200), and m (1 = m = 25). Inspection of the probability distributions indicated that confidence limits for m depended only on N whereas those for S o depended on both N and m. Whilst the determination of confidence limits for m proved to be relatively straightforward, the respective values for S o were obtained by fitting an empirical equation to the S o probability distributions approximated by a Gaussian curve. Example values of m and S o confidence limits for selected N have been presented in this work. 2017 Journal Article http://hdl.handle.net/20.500.11937/58210 10.1016/j.jeurceramsoc.2017.05.051 Elsevier Ltd restricted |
| spellingShingle | Davies, Ian Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title | Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title_full | Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title_fullStr | Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title_full_unstemmed | Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title_short | Confidence limits for Weibull parameters estimated using linear least squares analysis |
| title_sort | confidence limits for weibull parameters estimated using linear least squares analysis |
| url | http://hdl.handle.net/20.500.11937/58210 |