Functional Analysis Methods for Reliability Models

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.

lt;p>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)