On the structure of reliability polynomials

Christina Marie Graves, Syracuse University

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.