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    Multivariate discrete failure rates with some applications.

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    Author
    Valdez Torres, Jose Benigno.
    Issue Date
    1989
    Keywords
    Reliability (Engineering) -- Measurement
    Accelerated life testing
    Advisor
    Shaked, Moshe
    
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    Publisher
    The University of Arizona.
    Rights
    Copyright © 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.
    Abstract
    Throughout 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.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Applied Mathematics
    Graduate College
    Degree Grantor
    University of Arizona
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