Mathematical Theory Of Reliability
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| Author | : Richard E. Barlow |
| Publisher | : SIAM |
| Total Pages | : 271 |
| Release | : 1996-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0898713692 |
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 | : B. V. Gnedenko |
| Publisher | : Academic Press |
| Total Pages | : 519 |
| Release | : 2014-06-20 |
| Genre | : Mathematics |
| ISBN | : 1483263517 |
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 | : Simona Salicone |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 235 |
| Release | : 2007-06-04 |
| Genre | : Mathematics |
| ISBN | : 0387463283 |
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 | : Bo Lindqvist |
| Publisher | : World Scientific |
| Total Pages | : 569 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9812383212 |
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 | : V.V. Rykov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 465 |
| Release | : 2010-11-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0817649719 |
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 | : Arnljot Høyland |
| Publisher | : John Wiley & Sons |
| Total Pages | : 536 |
| Release | : 2009-09-25 |
| Genre | : Technology & Engineering |
| ISBN | : 0470317744 |
A comprehensive introduction to reliability analysis. The first section provides a thorough but elementary prologue to reliability theory. The latter half comprises more advanced analytical tools including Markov processes, renewal theory, life data analysis, accelerated life testing and Bayesian reliability analysis. Features numerous worked examples. Each chapter concludes with a selection of problems plus additional material on applications.
| Author | : Richard E. Barlow |
| Publisher | : SIAM |
| Total Pages | : 273 |
| Release | : 1996-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9781611971194 |
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. Mathematical reliability refers to a body of ideas, mathematical models, and methods directed toward the solution of problems in predicting, estimating, or optimizing the probability of survival, mean life, or, more generally, life distribution of components and systems. 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 republication. Unavailable since its original publication in 1965, Mathematical Theory of Reliability now joins a growing list of volumes in SIAM's Classics series. Although contemporary reliability books are now available, few provide as mathematically rigorous a treatment of the required probability background as this one.
| Author | : Jan Kåhre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 528 |
| Release | : 2002-06-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9781402070648 |
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 | : Jorge Navarro |
| Publisher | : Springer Nature |
| Total Pages | : 181 |
| Release | : 2021-10-03 |
| Genre | : Mathematics |
| ISBN | : 3030869539 |
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 | : Igor Bazovsky |
| Publisher | : Courier Corporation |
| Total Pages | : 322 |
| Release | : 2013-04-15 |
| Genre | : Mathematics |
| ISBN | : 0486317633 |
Written by a pioneer of reliability methods, this text applies statistical mathematics to analysis of electrical, mechanical, and other systems employed in airborne, missile, and ground equipment. 1961 edition.
