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Accelerated life testing and the Burr XII distribution. / RICHARD JOHNSON

Swansea University Author: RICHARD JOHNSON

Abstract

This thesis looks at extending previous work in the field of accelerated life testing experiments. Hitherto, much investigation in this field has centred on a few standard statistical lifetime distributions, the Weibull being particularly popular. We consider a more flexible distribution, the Burr X...

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Published: 2003
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42233
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spelling 2020-09-03T10:59:49.8189084 v2 42233 2018-08-02 Accelerated life testing and the Burr XII distribution. 11bc0c0dd28cb58bed00e99b2b2beabd RICHARD JOHNSON RICHARD JOHNSON true false 2018-08-02 This thesis looks at extending previous work in the field of accelerated life testing experiments. Hitherto, much investigation in this field has centred on a few standard statistical lifetime distributions, the Weibull being particularly popular. We consider a more flexible distribution, the Burr XII, and compare theoretical and simulated results; we also examine a number of examples. This comparison is interesting particularly since there is a limiting relationship between the two distributions, a property that is exploited in this thesis. Having laid down the necessary groundwork, we then proceed to fit the Weibull and Burr XH models to completely failed, published data sets and compare results. In order to assess our ability to make small sample theoretical inspections, we then establish the expected Fisher information matrices for the accelerated and non-accelerated Burr XH models, validating our results through simulations. The limiting link between the two distributions is then investigated, where we see that we can determine whether the Burr XH distribution will provide a better fit to a given data set than the Weibull, by fitting the Weibull distribution and then calculating a simple discriminating function. Type I censoring for the accelerated models is then considered. As for complete data, we formulate the expected Fisher information matrices. We then examine theoretical agreement between these results and those obtained for completely failed data. We also examine the agreement between Type I simulated and theoretical results. Finally, we investigate the practical applications of our work, and consider in particular extrapolations to lower operating stresses and the expected lifetimes of items tested at those stresses. Our investigations, although based on limited parameter values, illustrate useful conclusions on the conduct of such experiments and, consequently, are of potential value to a practitioner who, prior to carrying out an experiment, would like to know what combination of stresses and sample sizes would return the most information about the running time of items at the normal operating stress. After summarising our results and conclusions, some ideas for future research are detailed. E-Thesis Statistics. 31 12 2003 2003-12-31 COLLEGE NANME COLLEGE CODE Swansea University Doctoral Ph.D 2020-09-03T10:59:49.8189084 2018-08-02T16:24:28.5109848 Faculty of Humanities and Social Sciences School of Management - Business Management RICHARD JOHNSON 1 0042233-02082018162438.pdf 10797941.pdf 2018-08-02T16:24:38.5100000 Output 7894734 application/pdf E-Thesis true 2018-08-02T00:00:00.0000000 false
title Accelerated life testing and the Burr XII distribution.
spellingShingle Accelerated life testing and the Burr XII distribution.
RICHARD JOHNSON
title_short Accelerated life testing and the Burr XII distribution.
title_full Accelerated life testing and the Burr XII distribution.
title_fullStr Accelerated life testing and the Burr XII distribution.
title_full_unstemmed Accelerated life testing and the Burr XII distribution.
title_sort Accelerated life testing and the Burr XII distribution.
author_id_str_mv 11bc0c0dd28cb58bed00e99b2b2beabd
author_id_fullname_str_mv 11bc0c0dd28cb58bed00e99b2b2beabd_***_RICHARD JOHNSON
author RICHARD JOHNSON
author2 RICHARD JOHNSON
format E-Thesis
publishDate 2003
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 - Business Management{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Management - Business Management
document_store_str 1
active_str 0
description This thesis looks at extending previous work in the field of accelerated life testing experiments. Hitherto, much investigation in this field has centred on a few standard statistical lifetime distributions, the Weibull being particularly popular. We consider a more flexible distribution, the Burr XII, and compare theoretical and simulated results; we also examine a number of examples. This comparison is interesting particularly since there is a limiting relationship between the two distributions, a property that is exploited in this thesis. Having laid down the necessary groundwork, we then proceed to fit the Weibull and Burr XH models to completely failed, published data sets and compare results. In order to assess our ability to make small sample theoretical inspections, we then establish the expected Fisher information matrices for the accelerated and non-accelerated Burr XH models, validating our results through simulations. The limiting link between the two distributions is then investigated, where we see that we can determine whether the Burr XH distribution will provide a better fit to a given data set than the Weibull, by fitting the Weibull distribution and then calculating a simple discriminating function. Type I censoring for the accelerated models is then considered. As for complete data, we formulate the expected Fisher information matrices. We then examine theoretical agreement between these results and those obtained for completely failed data. We also examine the agreement between Type I simulated and theoretical results. Finally, we investigate the practical applications of our work, and consider in particular extrapolations to lower operating stresses and the expected lifetimes of items tested at those stresses. Our investigations, although based on limited parameter values, illustrate useful conclusions on the conduct of such experiments and, consequently, are of potential value to a practitioner who, prior to carrying out an experiment, would like to know what combination of stresses and sample sizes would return the most information about the running time of items at the normal operating stress. After summarising our results and conclusions, some ideas for future research are detailed.
published_date 2003-12-31T03:52:34Z
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score 11.013148

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