Mathematical Theory Of Reliability

Author : Richard E. Barlow,Frank Proschan
Publisher : SIAM
Page : 271 pages
File Size : 51,8 Mb
Release : 1996-01-01
Category : Technology & Engineering
ISBN : 9780898713695

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Mathematical Theory of Reliability by Richard E. Barlow,Frank Proschan Pdf

This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions - and only those based on plausible physical considerations - so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.

Author : Richard E. Barlow
Publisher : Unknown
Page : 128 pages
File Size : 51,6 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:861476615

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Mathematical Theory of Reliability by Richard E. Barlow Pdf

Author : B. V. Gnedenko,Yu. K. Belyayev,A. D. Solovyev
Publisher : Academic Press
Page : 518 pages
File Size : 48,9 Mb
Release : 2014-06-20
Category : Technology & Engineering
ISBN : 9781483263519

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Mathematical Methods of Reliability Theory by B. V. Gnedenko,Yu. K. Belyayev,A. D. Solovyev Pdf

Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles—redundancy. An important part of product quality control is the standards of acceptance-sampling plans which require simplicity, wide content for flexibility, comprehensive characteristics, and variability. The book also tackles economical and rational methods of sampling inspections, highlighting the need for a correct evaluation of environmental conditions—the factors which predetermine the choice of the inspection method. The book then explains how to estimate the efficiency of the operation of the sampling plan after its selection. The book can be helpful for engineers, mathematicians, economists, or industrial managers, as well as for other professionals who work in the technological, political, research, structural, and physico-chemical areas.

Author : Igor N. Kovalenko,Philip A. Pegg
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 47,7 Mb
Release : 1997-07-16
Category : Mathematics
ISBN : STANFORD:36105019810675

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Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications by Igor N. Kovalenko,Philip A. Pegg Pdf

One of the greatest problems in engineering is reliability. The performance of all machinery degrades over time and unless counteraction is taken at some point, any system will eventually fail. Once a system fails there are a number of possible solutions; the mathematical and statistical measurement and analysis of these solutions forms the mathematical theory of reliability. The aim of the authors is to concentrate on aspects of particular importance in the mathematical theory of reliability of time dependent systems rather than give a general overview. Particular emphasis is placed on fault tree analysis, Monte Carlo methods and importance measures. This book will be of particular interest to applied researchers and engineers working in areas where reliability is crucial. Contents Introduction, Markov and Semi-Markov models as a basis for the mathematical analysis of system reliability, methods for investigating homogeneous and non-homogeneous point processes (event flows), fault trees ? the current state of research, theory of redundant systems, Monte Carlo methods, reliability analysis using perturbation methods, stiff processes in reliability analysis, variance reduction methods, analytical-statistical methods for rapid simulation of repairable systems with structure redundancy, measures of reliability importance of components, index.

Author : Bo Lindqvist,Kjell A. Doksum
Publisher : World Scientific
Page : 569 pages
File Size : 49,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812383211

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Mathematical and Statistical Methods in Reliability by Bo Lindqvist,Kjell A. Doksum Pdf

This book contains extended versions of carefully selected and reviewed papers presented at the Third International Conference on Mathematical Methods in Reliability, held in Norway in 2002. It provides an overview of current research activities in reliability theory. The authors are all leading experts in the field. Readership: Graduate students, academics and professionals in probability & statistics, reliability analysis, survival analysis, industrial engineering, software engineering, operations research and applied mathematics research.

Author : Jorge Navarro
Publisher : Springer Nature
Page : 181 pages
File Size : 55,6 Mb
Release : 2021-10-03
Category : Mathematics
ISBN : 9783030869533

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Introduction to System Reliability Theory by Jorge Navarro Pdf

This textbook provides the tools for a modern post-graduate introductory course on system reliability theory. It focuses on probabilistic aspects of the theory, including recent results based on signatures, stochastic orders, aging classes, copulas and distortion (or aggregation) functions. The reader requires on an introductory knowledge on probability theory and mathematics. The book serves both for graduate students in mathematics and for engineering students in various disciplines as well as students learning survival analysis, network reliability or simple game theory. Included also are brief introductions to the basic aspects of lifetime modelling, stochastic comparisons, aging classes, mixtures and copula theory. The book develops this knowledge with worked examples and supplies code for the program R so that students can explore its lessons and techniques.

Author : Simona Salicone
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 48,9 Mb
Release : 2007-06-04
Category : Mathematics
ISBN : 9780387463285

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Measurement Uncertainty by Simona Salicone Pdf

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book’s unique approach.

Author : V.V. Rykov,N. Balakrishnan,M.S. Nikulin
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 44,9 Mb
Release : 2010-11-02
Category : Technology & Engineering
ISBN : 9780817649715

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Mathematical and Statistical Models and Methods in Reliability by V.V. Rykov,N. Balakrishnan,M.S. Nikulin Pdf

The book is a selection of invited chapters, all of which deal with various aspects of mathematical and statistical models and methods in reliability. Written by renowned experts in the field of reliability, the contributions cover a wide range of applications, reflecting recent developments in areas such as survival analysis, aging, lifetime data analysis, artificial intelligence, medicine, carcinogenesis studies, nuclear power, financial modeling, aircraft engineering, quality control, and transportation. Mathematical and Statistical Models and Methods in Reliability is an excellent reference text for researchers and practitioners in applied probability and statistics, industrial statistics, engineering, medicine, finance, transportation, the oil and gas industry, and artificial intelligence.

Author : Benjamin Epstein,Ishay Weissman
Publisher : CRC Press
Page : 272 pages
File Size : 47,8 Mb
Release : 2008-05-09
Category : Mathematics
ISBN : 1420080830

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Mathematical Models for Systems Reliability by Benjamin Epstein,Ishay Weissman Pdf

Evolved from the lectures of a recognized pioneer in developing the theory of reliability, Mathematical Models for Systems Reliability provides a rigorous treatment of the required probability background for understanding reliability theory. This classroom-tested text begins by discussing the Poisson process and its associated probability laws. It then uses a number of stochastic models to provide a framework for life length distributions and presents formal rules for computing the reliability of nonrepairable systems that possess commonly occurring structures. The next two chapters explore the stochastic behavior over time of one- and two-unit repairable systems. After covering general continuous-time Markov chains, pure birth and death processes, and transitions and rates diagrams, the authors consider first passage-time problems in the context of systems reliability. The final chapters show how certain techniques can be applied to a variety of reliability problems. Illustrating the models and methods with a host of examples, this book offers a sound introduction to mathematical probabilistic models and lucidly explores how they are used in systems reliability problems.

Author : N. Limnios,M. Nikulin
Publisher : Springer Science & Business Media
Page : 515 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461213840

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Recent Advances in Reliability Theory by N. Limnios,M. Nikulin Pdf

This book presents thirty-one extensive and carefully edited chapters providing an up-to-date survey of new models and methods for reliability analysis and applications in science, engineering, and technology. The chapters contain broad coverage of the latest developments and innovative techniques in a wide range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.

Author : Jan Kåhre
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 53,8 Mb
Release : 2002-06-30
Category : Technology & Engineering
ISBN : 1402070640

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The Mathematical Theory of Information by Jan Kåhre Pdf

The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.

Author : Juerg Kohlas,Paul-Andre Monney
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 42,8 Mb
Release : 2013-11-11
Category : Business & Economics
ISBN : 9783662016749

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A Mathematical Theory of Hints by Juerg Kohlas,Paul-Andre Monney Pdf

An approach to the modeling of and the reasoning under uncertainty. The book develops the Dempster-Shafer Theory with regard to the reliability of reasoning with uncertain arguments. Of particular interest here is the development of a new synthesis and the integration of logic and probability theory. The reader benefits from a new approach to uncertainty modeling which extends classical probability theory.

Author : Claude E Shannon,Warren Weaver
Publisher : University of Illinois Press
Page : 144 pages
File Size : 52,9 Mb
Release : 1998-09-01
Category : Language Arts & Disciplines
ISBN : 9780252098031

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The Mathematical Theory of Communication by Claude E Shannon,Warren Weaver Pdf

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

Author : Alyson G. Wilson
Publisher : World Scientific
Page : 428 pages
File Size : 44,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703378

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Modern Statistical and Mathematical Methods in Reliability by Alyson G. Wilson Pdf

This volume contains extended versions of 28 carefully selected and reviewed papers presented at The Fourth International Conference on Mathematical Methods in Reliability in Santa Fe, New Mexico, June 21OCo25, 2004, the leading conference in reliability research. The meeting serves as a forum for discussing fundamental issues on mathematical methods in reliability theory and its applications. A broad overview of current research activities in reliability theory and its applications is provided with coverage on reliability modeling, network and system reliability, Bayesian methods, survival analysis, degradation and maintenance modeling, and software reliability. The contributors are all leading experts in the field and include the plenary session speakers, Tim Bedford, Thierry Duchesne, Henry Wynn, Vicki Bier, Edsel Pena, Michael Hamada, and Todd Graves."

Author : Ajit Kumar Verma,Srividya Ajit,Durga Rao Karanki
Publisher : Springer
Page : 571 pages
File Size : 43,5 Mb
Release : 2015-09-28
Category : Technology & Engineering
ISBN : 9781447162698

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Reliability and Safety Engineering by Ajit Kumar Verma,Srividya Ajit,Durga Rao Karanki Pdf

Reliability and safety are core issues that must be addressed throughout the life cycle of engineering systems. Reliability and Safety Engineering presents an overview of the basic concepts, together with simple and practical illustrations. The authors present reliability terminology in various engineering fields, viz., electronics engineering, software engineering, mechanical engineering, structural engineering and power systems engineering. The book describes the latest applications in the area of probabilistic safety assessment, such as technical specification optimization, risk monitoring and risk informed in-service inspection. Reliability and safety studies must, inevitably, deal with uncertainty, so the book includes uncertainty propagation methods: Monte Carlo simulation, fuzzy arithmetic, Dempster-Shafer theory and probability bounds. Reliability and Safety Engineering also highlights advances in system reliability and safety assessment including dynamic system modeling and uncertainty management. Case studies from typical nuclear power plants as well as from structural, software and electronic systems are also discussed. Reliability and Safety Engineering combines discussions of the existing literature on basic concepts and applications with state-of-the-art methods used in reliability and risk assessment of engineering systems. It is designed to assist practicing engineers, students and researchers in the areas of reliability engineering and risk analysis.