Probabilistic Reliability Models

A comprehensively updated and reorganized new edition. The updates include comparative methods for improving reliability; methods for optimal allocation of limited resources to achieve a maximum risk reduction; methods for improving reliability at no extra cost and building reliability networks for engineering systems. Includes: A unique set of 46 generic principles for reducing technical risk Monte Carlo simulation algorithms for improving reliability and reducing risk Methods for setting reliability requirements based on the cost of failure New reliability measures based on a minimal separation of random events on a time interval Overstress reliability integral for determining the time to failure caused by overstress failure modes A powerful equation for determining the probability of failure controlled by defects in loaded components with complex shape Comparative methods for improving reliability which do not require reliability data Optimal allocation of limited resources to achieve a maximum risk reduction Improving system reliability based solely on a permutation of interchangeable components

The leading reference on probabilistic methods in combinatorics-now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications. The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or «probabilistic lenses,» are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes: * Several improved as well as new results * A continuous approach to discrete probabilistic problems * Talagrand's Inequality and other novel concentration results * A discussion of the connection between discrepancy and VC-dimension * Several combinatorial applications of the entropy function and its properties * A new section on the life and work of Paul Erd?s-the developer of the probabilistic method

Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” – MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The G?del Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

The book is composed of 12 chapters and three appendices, and can be divided into four parts. The first part includes Chapters 2 to 7, which discuss the concepts, models, methods and data in probabilistic transmission planning. The second part, Chapters 8 to 11, addresses four essential issues in probabilistic transmission planning applications using actual utility systems as examples. Chapter 12, as the third part, focuses on a special issue, i.e. how to deal with uncertainty of data in probabilistic transmission planning. The fourth part consists of three appendices, which provide the basic knowledge in mathematics for probabilistic planning.

An Integrated Approach to Product Development Reliability Engineering presents an integrated approach to the design, engineering, and management of reliability activities throughout the life cycle of a product, including concept, research and development, design, manufacturing, assembly, sales, and service. Containing illustrative guides that include worked problems, numerical examples, homework problems, a solutions manual, and class-tested materials, it demonstrates to product development and manufacturing professionals how to distribute key reliability practices throughout an organization. The authors explain how to integrate reliability methods and techniques in the Six Sigma process and Design for Six Sigma (DFSS). They also discuss relationships between warranty and reliability, as well as legal and liability issues. Other topics covered include: Reliability engineering in the 21st Century Probability life distributions for reliability analysis Process control and process capability Failure modes, mechanisms, and effects analysis Health monitoring and prognostics Reliability tests and reliability estimation Reliability Engineering provides a comprehensive list of references on the topics covered in each chapter. It is an invaluable resource for those interested in gaining fundamental knowledge of the practical aspects of reliability in design, manufacturing, and testing. In addition, it is useful for implementation and management of reliability programs.

We all like to know how reliable and how risky certain situations are, and our increasing reliance on technology has led to the need for more precise assessments than ever before. Such precision has resulted in efforts both to sharpen the notions of risk and reliability, and to quantify them. Quantification is required for normative decision-making, especially decisions pertaining to our safety and wellbeing. Increasingly in recent years Bayesian methods have become key to such quantifications. Reliability and Risk provides a comprehensive overview of the mathematical and statistical aspects of risk and reliability analysis, from a Bayesian perspective. This book sets out to change the way in which we think about reliability and survival analysis by casting them in the broader context of decision-making. This is achieved by: Providing a broad coverage of the diverse aspects of reliability, including: multivariate failure models, dynamic reliability, event history analysis, non-parametric Bayes, competing risks, co-operative and competing systems, and signature analysis. Covering the essentials of Bayesian statistics and exchangeability, enabling readers who are unfamiliar with Bayesian inference to benefit from the book. Introducing the notion of “composite reliability”, or the collective reliability of a population of items. Discussing the relationship between notions of reliability and survival analysis and econometrics and financial risk. Reliability and Risk can most profitably be used by practitioners and research workers in reliability and survivability as a source of information, reference, and open problems. It can also form the basis of a graduate level course in reliability and risk analysis for students in statistics, biostatistics, engineering (industrial, nuclear, systems), operations research, and other mathematically oriented scientists, wherein the instructor could supplement the material with examples and problems.

This title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Those who possess a sound knowledge of the subject mater will find the title of great interest, but those who have only some mathematical familiarity and knowledge about complexity and approximation theory will also find it an accessible and informative read.

A unique, design-based approach to reliability engineering Design for Reliability provides engineers and managers with a range of tools and techniques for incorporating reliability into the design process for complex systems. It clearly explains how to design for zero failure of critical system functions, leading to enormous savings in product life-cycle costs and a dramatic improvement in the ability to compete in global markets. Readers will find a wealth of design practices not covered in typical engineering books, allowing them to think outside the box when developing reliability requirements. They will learn to address high failure rates associated with systems that are not properly designed for reliability, avoiding expensive and time-consuming engineering changes, such as excessive testing, repairs, maintenance, inspection, and logistics. Special features of this book include: A unified approach that integrates ideas from computer science and reliability engineering Techniques applicable to reliability as well as safety, maintainability, system integration, and logistic engineering Chapters on design for extreme environments, developing reliable software, design for trustworthiness, and HALT influence on design Design for Reliability is a must-have guide for engineers and managers in R&D, product development, reliability engineering, product safety, and quality assurance, as well as anyone who needs to deliver high product performance at a lower cost while minimizing system failure.

Learn how to model, predict, and manage system reliability/availability throughout the development life cycle Written by a panel of authors with a wealth of industry experience, the methods and concepts presented here give readers a solid understanding of modeling and managing system and software availability and reliability through the development of real applications and products. The modeling and prediction techniques and tools are customer-focused and data-driven, and are also aligned with industry standards (Telcordia, TL 9000, ISO, etc.). Readers will get a clear understanding about what real-world reliability and availability mean through step-by-step discussions of: System availability Conceptual model of reliability and availability Why availability varies between customers Modeling availability Estimating parameters and availability from field data Estimating input parameters from laboratory data Estimating input parameters in the architecture/design stage Prediction accuracy Connecting the dots This book can be used by system architects, engineers, and developers to better understand and manage the reliability/availability of their products; quality engineers to grasp how software and hardware quality relate to system availability; and engineering students as part of a short course on system availability and software reliability.

Provides practical guidance on the latest quality assurance and accelerated stress test methods for improved long-term performance prediction of PV modules This book has been written from a historical perspective to guide readers through how the PV industry learned what the failure and degradation modes of PV modules were, how accelerated tests were developed to cause the same failures and degradations in the laboratory, and then how these tests were used as tools to guide the design and fabrication of reliable and long-life modules. Photovoltaic Module Reliability starts with a brief history of photovoltaics, discussing some of the different types of materials and devices used for commercial solar cells. It then goes on to offer chapters on: Module Failure Modes; Development of Accelerated Stress Tests; Qualification Testing; and Failure Analysis Tools. Next, it examines the use of quality management systems to manufacture PV modules. Subsequent chapters cover the PVQAT Effort; the Conformity Assessment and IECRE; and Predicting PV Module Service Life. The book finishes with a look at what the future holds for PV. A comprehensive treatment of current photovoltaic (PV) technology reliability and necessary improvement to become a significant part of the electric utility supply system Well documented with experimental and practical cases throughout, enhancing relevance to both scientific community and industry Timely contribution to the harmonization of methodological aspects of PV reliability evaluation with test procedures implemented to certify PV module quality Written by a leading international authority in PV module reliability Photovoltaic Module Reliability is an excellent book for anyone interested in PV module reliability, including those working directly on PV module and system reliability and preparing to purchase modules for deployment.