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dc.contributor.advisorShaked, Mosheen_US
dc.contributor.authorValdez Torres, Jose Benigno.
dc.creatorValdez Torres, Jose Benigno.en_US
dc.date.accessioned2011-10-31T17:22:40Z
dc.date.available2011-10-31T17:22:40Z
dc.date.issued1989en_US
dc.identifier.urihttp://hdl.handle.net/10150/184929
dc.description.abstractThroughout this work, conditional failure rates for discrete positive integer-valued random variables and some of their applications are considered in some detail. Conditional failure rates are of fundamental importance in the study of lifetime distributions and many of their properties. All the notions introduced and the results derived here can be used in reliability theory, operations research, inventory theory, biometry, etc. Chapter 1 begins with the concept of conditional failure rate of a discrete random variable. Then, it is shown how to obtain explicit expressions for probability densities and survival distributions in terms of this notion. Next, extensions of the univariate results are discussed for bivariate discrete random vectors. Finally, some multivariate concepts and results are outlined. One of the fundamental applications of conditional failure rates is the mathematical representation of ageing. In Chapter 2, several univariate notions of ageing are given for discrete random variables. Such notions constitute the starting point for the classification and study of lifetime distributions that have significant importance in reliability theory, biometry, and several other areas. In Chapter 3, three important ordering relations, and a chain of implications among them, are discussed; the likelihood ratio ordering, the failure rate ordering, and the stochastic ordering. These orderings are useful in applied probability, stochastic processes, statistics, etc. In particular, they are an essential tool in the study and analysis of systems with dependent components, specially when the components are associated. No attempt is made, however, to consider specific applications of these orderings here. Finally, Chapter 4 contains an application of conditional failure rates in the analysis of repairable systems. A random mechanism of repair of failed units, called imperfect repair, is introduced and some simplified models are considered in some extent. These models can be used in the analysis and design of maintenance policies.
dc.language.isoenen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectReliability (Engineering) -- Measurementen_US
dc.subjectAccelerated life testingen_US
dc.titleMultivariate discrete failure rates with some applications.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.identifier.oclc703606258en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.contributor.committeememberFaris, William G.en_US
dc.contributor.committeememberWright, A. Larryen_US
dc.identifier.proquest9013185en_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.namePh.D.en_US
refterms.dateFOA2018-08-22T22:48:25Z
html.description.abstractThroughout this work, conditional failure rates for discrete positive integer-valued random variables and some of their applications are considered in some detail. Conditional failure rates are of fundamental importance in the study of lifetime distributions and many of their properties. All the notions introduced and the results derived here can be used in reliability theory, operations research, inventory theory, biometry, etc. Chapter 1 begins with the concept of conditional failure rate of a discrete random variable. Then, it is shown how to obtain explicit expressions for probability densities and survival distributions in terms of this notion. Next, extensions of the univariate results are discussed for bivariate discrete random vectors. Finally, some multivariate concepts and results are outlined. One of the fundamental applications of conditional failure rates is the mathematical representation of ageing. In Chapter 2, several univariate notions of ageing are given for discrete random variables. Such notions constitute the starting point for the classification and study of lifetime distributions that have significant importance in reliability theory, biometry, and several other areas. In Chapter 3, three important ordering relations, and a chain of implications among them, are discussed; the likelihood ratio ordering, the failure rate ordering, and the stochastic ordering. These orderings are useful in applied probability, stochastic processes, statistics, etc. In particular, they are an essential tool in the study and analysis of systems with dependent components, specially when the components are associated. No attempt is made, however, to consider specific applications of these orderings here. Finally, Chapter 4 contains an application of conditional failure rates in the analysis of repairable systems. A random mechanism of repair of failed units, called imperfect repair, is introduced and some simplified models are considered in some extent. These models can be used in the analysis and design of maintenance policies.


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