Title

On the structure of reliability polynomials

Date of Award

2009

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Jack E. Graver

Keywords

Reliability polynomials, Convex basis, Inflection point

Subject Categories

Physical Sciences and Mathematics

Abstract

This dissertation explores a new way to look at reliability polynomials by use of a convex basis. The shape of reliability polynomials has been studied by numerous people including Moore, Shannon, Birnbaum, Esary, Saunders, and Colbourn. Colbourn posed the question, "Is it true that a reliability polynomial has at most one point of inflection in the range p ∈ (0; 1)?" This newly created convex basis allows us to consider the inflection point problem from a new viewpoint. In fact, it is used to deduce that reliability polynomials can have more than one inflection point.

Comments

ISBN 9781109463033

Access

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