On the structure of reliability polynomials
Date of Award
Doctor of Philosophy (PhD)
Jack E. Graver
Reliability polynomials, Convex basis, Inflection point
Physical Sciences and Mathematics
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.
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Graves, Christina Marie, "On the structure of reliability polynomials" (2009). Mathematics - Dissertations. Paper 8.