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Mathematical Models for Systems Reliability

Mathematical Models for Systems Reliability
Author: Benjamin Epstein
Publisher: CRC Press
Total Pages: 272
Release: 2019-08-30
Genre:
ISBN: 9780367387327

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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.


Mathematical Models for Systems Reliability

Mathematical Models for Systems Reliability
Author: Benjamin Epstein
Publisher: CRC Press
Total Pages: 270
Release: 2008-05-09
Genre: Business & Economics
ISBN: 1420080830

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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


Mathematical and Statistical Models and Methods in Reliability

Mathematical and Statistical Models and Methods in Reliability
Author: V.V. Rykov
Publisher: Springer Science & Business Media
Total Pages: 465
Release: 2010-11-02
Genre: Technology & Engineering
ISBN: 0817649719

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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.


Introduction to System Reliability Theory

Introduction to System Reliability Theory
Author: Jorge Navarro
Publisher: Springer Nature
Total Pages: 181
Release: 2021-10-03
Genre: Mathematics
ISBN: 3030869539

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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.


Mathematical Models for Structural Reliability Analysis

Mathematical Models for Structural Reliability Analysis
Author: Fabio Casciati
Publisher: CRC Press
Total Pages: 386
Release: 1996-07-24
Genre: Mathematics
ISBN: 9780849396311

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Mathematical Models for Structural Reliability Analysis offers mathematical models for describing load and material properties in solving structural engineering problems. Examples are provided, demonstrating how the models are implemented, and the limitations of the models are clearly stated. Analytical solutions are also discussed, and methods are clearly distinguished from models. The authors explain both theoretical models and practical applications in a clear, concise, and readable fashion.


Mathematical Theory of Reliability

Mathematical Theory of Reliability
Author: Richard E. Barlow
Publisher: SIAM
Total Pages: 271
Release: 1996-01-01
Genre: Technology & Engineering
ISBN: 0898713692

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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.


Mathematical Modelling of System Resilience

Mathematical Modelling of System Resilience
Author: Kanchan Das
Publisher:
Total Pages: 0
Release: 2023-05-31
Genre: Reliability (Engineering)
ISBN: 9788770229685

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Each of the chapters contributes state of the art research for the relevant resilience related topic covered in the chapter.


Assessing the Reliability of Complex Models

Assessing the Reliability of Complex Models
Author: National Research Council
Publisher: National Academies Press
Total Pages: 144
Release: 2012-07-26
Genre: Mathematics
ISBN: 0309256348

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Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.