Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485598
Title: Characterisations of life distributions with applications in reliability theory
Author: Al-Zahrani, Bander M.
ISNI:       0000 0001 3409 4955
Awarding Body: Newcastle University
Current Institution: University of Newcastle upon Tyne
Date of Award: 2008
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Abstract:
The present work is in the area of Reliability Analysis. It is widely regarded that this is among the important areas of Modern Applied Probability and Statistics. Rel,iability theory involves a comprehensive analysis of classes of distributions describing the random time of proper functioning before the failure of a component, device, etc. This theory is known as Sur~ival Analysis in biomedical studies and Duration Analysis in economics. It has been also used in demography, queuing theory, actuarial sciences, engineering maintenance and replacement policies. Our research is focused on classes of continuous and discrete life distributions defined in terms of functions which are the main characteristics, namely, the failure rate, the mean residual lifetime, and the variance residual lifetime. Recent studies showed how important is to work with the residual variance. We study in detail models with specific shape of variance. vVe also give characterisations for aging classes consisting of log-concave life distributions. We study also different classes of discrete life distributions. V'le provide fur- ' ther properties for the geometric distribution based on constant variance residual lifetimes. Another object of recent interest is the reversed residual lifetime. The properties of the reversed failure rate have become a topic of interest not only in reliability, but also in other fields. vVe focus on properties of the reversed variance - . residual lifetime and the interrelations among reversed ageing classes. Life testing problems are central in Reliability theory because of their importance for practice. Testing exponentiality versus some ageing classes is discussed from a new point of view. We consider two types of test statistics: the empirical test statistic, and tests based on moment inequalities. Some sort of V-statistics is proposed in both cases. During this study, some new results have been obtained. They are included with all the details and illustrations. Our results are well comparable with existing results in the literature. Some of our tests for exponentiality are better than widely used tests.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.485598  DOI: Not available
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