Functional Analysis Methods for Reliability Models / Edition 1

by Geni Gupur

Overview

The main goal of this book is to introduce readers to functional analysis methods, in particular, time dependent analysis, for reliability models. Understanding the concept of reliability is of key importance – schedule delays, inconvenience, customer dissatisfaction, and loss of prestige and even weakening of national security are common examples of results that are caused by unreliability of systems and individuals.

The book begins with an introduction to C₀-semigroup theory. Then, after a brief history of reliability theory, methods that study the well-posedness, the asymptotic behaviors of solutions and reliability indices for varied reliability models are presented. Finally, further research problems are explored.

Functional Analysis Methods for Reliability Models is an excellent reference for graduate students and researchers in operations research, applied mathematics and systems engineering.

Product Details

ISBN-13:	9783034801003
Publisher:	Springer Basel
Publication date:	07/08/2011
Series:	Pseudo-Differential Operators , #6
Edition description:	2011
Pages:	277
Product dimensions:	6.61(w) x 9.45(h) x 0.03(d)

Table of Contents

Preface.- C₀-Semigroup of Linear Operators and Cauchy Problems.- Statement of the Problems.- The System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity.- Transfer Line Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Infinite Capacity.- Further Research Problems.- Bibliography.

Editorial Reviews

From the reviews:

“The main goal of this monograph is to introduce the reader to methods of linear functional analysis useful for studying contemporary reliability models. … The book will be definitely of interest for specialists in queuing theory, in mathematical modelling of complex manufacturing systems and for all interested in applications of semigroups methods to integro-differential equations. The volume can be read by anyone with a basic knowledge of probability theory and linear functional analysis.” (Mikhail Yu. Kokurin, Zentralblatt MATH, Vol. 1223, 2011)

“This book focuses on mathematical methodologies for reliability theory, with emphasis on theory and methods of functional analysis for shastic models in reliability. … this monograph provides a detailed study of some Markov processes describing an integrated manufacturing system. The mathematical analysis is based on useful methods of functional analysis, concerning pseudo-differential operators and infinite-dimensional tridiagonal matrices.” (Antonio Di Crescenzo, Mathematical Reviews, Issue 2012 h)

From the Publisher