© 2011

Functional Analysis Methods for Reliability Models


Part of the Pseudo-Differential Operators book series (PDO, volume 6)

About this book


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.

Authors and affiliations

  1. 1., College of Mathematics and Systems ScienXinjiang UniversityUrumqiChina, People's Republic

Bibliographic information


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 stochastic 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)