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Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data. / Hannah K Finselbach

Swansea University Author: Hannah K Finselbach

Abstract

This thesis looks at extending previous work in the field of Type I censored reliability experiments. Due to its popularity and wide use, we use the Weibull distribution, and provide formulae on asymptotically valid variances and covariance of the maximum likelihood estimates and quantiles. We also...

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Published: 2007
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42331
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first_indexed 2018-08-02T18:54:27Z
last_indexed 2018-08-03T10:09:52Z
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spelling 2018-08-02T16:24:28.8541953 v2 42331 2018-08-02 Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data. 3675a447c56be5930027f8847e0ca34e NULL Hannah K Finselbach Hannah K Finselbach true true 2018-08-02 This thesis looks at extending previous work in the field of Type I censored reliability experiments. Due to its popularity and wide use, we use the Weibull distribution, and provide formulae on asymptotically valid variances and covariance of the maximum likelihood estimates and quantiles. We also examine the effect that sample size and censoring levels have on such properties. Theoretical results are validated with simulation studies throughout. These results are then used to obtain measures of precision in the Weibull parameter and quantile estimates given the assumption of asymptotic Normality. The suitability of using this large sample Normal theory in finite samples is consequently studied, and we provide an alternative measure of precision using relative likelihood methods. Confidence regions for each method are compared using published data. We investigate the concept of undertaking interim analysis of reliability data, where maximum likelihood estimates are calculated at successive times during an experiment, but the experiment is only stopped when adequate precision in the censored estimate is obtained. That is, when the censored estimate can provide a reliable guide to the complete estimate. Finally we summarise our results and conclusions, and some ideas for future research are discussed. E-Thesis Statistics. 31 12 2007 2007-12-31 COLLEGE NANME Economics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:28.8541953 2018-08-02T16:24:28.8541953 Faculty of Humanities and Social Sciences School of Management - Economics Hannah K Finselbach NULL 1 0042331-02082018162446.pdf 10798039.pdf 2018-08-02T16:24:46.0300000 Output 5365103 application/pdf E-Thesis true 2018-08-02T16:24:46.0300000 false
title Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
spellingShingle Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
Hannah K Finselbach
title_short Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
title_full Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
title_fullStr Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
title_full_unstemmed Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
title_sort Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data.
author_id_str_mv 3675a447c56be5930027f8847e0ca34e
author_id_fullname_str_mv 3675a447c56be5930027f8847e0ca34e_***_Hannah K Finselbach
author Hannah K Finselbach
author2 Hannah K Finselbach
format E-Thesis
publishDate 2007
institution Swansea University
college_str Faculty of Humanities and Social Sciences
hierarchytype
hierarchy_top_id facultyofhumanitiesandsocialsciences
hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Management - Economics{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Management - Economics
document_store_str 1
active_str 0
description This thesis looks at extending previous work in the field of Type I censored reliability experiments. Due to its popularity and wide use, we use the Weibull distribution, and provide formulae on asymptotically valid variances and covariance of the maximum likelihood estimates and quantiles. We also examine the effect that sample size and censoring levels have on such properties. Theoretical results are validated with simulation studies throughout. These results are then used to obtain measures of precision in the Weibull parameter and quantile estimates given the assumption of asymptotic Normality. The suitability of using this large sample Normal theory in finite samples is consequently studied, and we provide an alternative measure of precision using relative likelihood methods. Confidence regions for each method are compared using published data. We investigate the concept of undertaking interim analysis of reliability data, where maximum likelihood estimates are calculated at successive times during an experiment, but the experiment is only stopped when adequate precision in the censored estimate is obtained. That is, when the censored estimate can provide a reliable guide to the complete estimate. Finally we summarise our results and conclusions, and some ideas for future research are discussed.
published_date 2007-12-31T03:52:45Z
_version_ 1763752611059597312
score 11.037056

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