Pseudo-Differential Operators

Functional Analysis Methods for Reliability Models

Authors: Gupur, Geni

  • Covers reliability models pertinent to daily life
  • Explains the mathematics of reliability
  • Discusses functional analysis methods
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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.

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 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)


Table of contents (5 chapters)

  • C 0-Semigroups of Linear Operators and Cauchy Problems

    Gupur, Geni

    Pages 1-48

  • Statement of the Problems

    Gupur, Geni

    Pages 49-58

  • The System Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Finite Capacity

    Gupur, Geni

    Pages 59-135

  • Transfer Line Consisting of a Reliable Machine, an Unreliable Machine and a Storage Buffer with Infinite Capacity

    Gupur, Geni

    Pages 137-258

  • Further Research Problems

    Gupur, Geni

    Pages 259-266

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0101-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-0348-0100-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Functional Analysis Methods for Reliability Models
Authors
Series Title
Pseudo-Differential Operators
Series Volume
6
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0101-0
DOI
10.1007/978-3-0348-0101-0
Softcover ISBN
978-3-0348-0100-3
Series ISSN
2297-0355
Edition Number
1
Number of Pages
VIII, 277
Topics