#### 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.

#### Access

Surface provides description only. Full text is available to ProQuest subscribers. Ask your Librarian for assistance.

#### Recommended Citation

Graves, Christina Marie, "On the structure of reliability polynomials" (2009). *Mathematics - Dissertations.* Paper 8.

http://surface.syr.edu/mat_etd/8

http://libezproxy.syr.edu/login?url=http://proquest.umi.com/pqdweb?did=1906514951&sid=1&Fmt=2&clientId=3739&RQT=309&VName=PQD

## Comments

ISBN 9781109463033