Statistical Analysis Of Reliability Data

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Written for those who have taken a first course in statistical methods, this book takes a modern, computer-oriented approach to describe the statistical techniques used for the assessment of reliability.

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Genre : Business & Economics
Author : Martin J. Crowder
Publisher : Routledge
Release : 2017-11-13
File : 268 Pages
ISBN-13 : 9781351414616


Statistical Methods For Reliability Data

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An authoritative guide to the most recent advances in statistical methods for quantifying reliability Statistical Methods for Reliability Data, Second Edition (SMRD2) is an essential guide to the most widely used and recently developed statistical methods for reliability data analysis and reliability test planning. Written by three experts in the area, SMRD2 updates and extends the long- established statistical techniques and shows how to apply powerful graphical, numerical, and simulation-based methods to a range of applications in reliability. SMRD2 is a comprehensive resource that describes maximum likelihood and Bayesian methods for solving practical problems that arise in product reliability and similar areas of application. SMRD2 illustrates methods with numerous applications and all the data sets are available on the book’s website. Also, SMRD2 contains an extensive collection of exercises that will enhance its use as a course textbook. The SMRD2's website contains valuable resources, including R packages, Stan model codes, presentation slides, technical notes, information about commercial software for reliability data analysis, and csv files for the 93 data sets used in the book's examples and exercises. The importance of statistical methods in the area of engineering reliability continues to grow and SMRD2 offers an updated guide for, exploring, modeling, and drawing conclusions from reliability data. SMRD2 features: Contains a wealth of information on modern methods and techniques for reliability data analysis Offers discussions on the practical problem-solving power of various Bayesian inference methods Provides examples of Bayesian data analysis performed using the R interface to the Stan system based on Stan models that are available on the book's website Includes helpful technical-problem and data-analysis exercise sets at the end of every chapter Presents illustrative computer graphics that highlight data, results of analyses, and technical concepts Written for engineers and statisticians in industry and academia, Statistical Methods for Reliability Data, Second Edition offers an authoritative guide to this important topic.

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Genre : Technology & Engineering
Author : William Q. Meeker
Publisher : John Wiley & Sons
Release : 2021-12-29
File : 708 Pages
ISBN-13 : 9781118115459


Practical Methods For Reliability Data Analysis

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This practical introduction to the analysis of data collected from reliability studies offers clear, detailed explanations of the best and most up-to-date techniques available. Topics include survival analysis with covariates, the assessment of systems performance, reliability growth models, dependency (which encompasses both engineering and statistical approaches), and practical aspects of analysis. A wealth of interesting case studies appear throughout the text, lending "real-world" examples to the more theoretical discussions. Throughout, the authors stress the need for investigators to understand the background and nature of their data if they are to select the most appropriate analysis method. They also provide in-depth treatments of the mathematical and statistical bases underlying each technique. Accessible and comprehensive, the book will be welcomed by students, professionals, and statisticians who are interested in the practical aspects of reliability data analysis.

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Genre : Mathematics
Author : Jake Ansell
Publisher : Oxford University Press
Release : 1994
File : 264 Pages
ISBN-13 : 019853664X


The Theory Of Measures And Integration

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An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry. Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include: * Measurable Functions * The Lp Spaces * The Radon-Nikodym Theorem * Products of Two Measure Spaces * Arbitrary Products of Measure Spaces Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics. In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.

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Genre : Mathematics
Author : Eric M. Vestrup
Publisher : John Wiley & Sons
Release : 2009-09-25
File : 622 Pages
ISBN-13 : 9780470317952


The Subjectivity Of Scientists And The Bayesian Approach

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Comparing and contrasting the reality of subjectivity in the workof history's great scientists and the modern Bayesian approach tostatistical analysis Scientists and researchers are taught to analyze their data from anobjective point of view, allowing the data to speak for themselvesrather than assigning them meaning based on expectations oropinions. But scientists have never behaved fully objectively.Throughout history, some of our greatest scientific minds haverelied on intuition, hunches, and personal beliefs to make sense ofempirical data-and these subjective influences have often aided inhumanity's greatest scientific achievements. The authors argue thatsubjectivity has not only played a significant role in theadvancement of science, but that science will advance more rapidlyif the modern methods of Bayesian statistical analysis replace someof the classical twentieth-century methods that have traditionallybeen taught. To accomplish this goal, the authors examine the lives and work ofhistory's great scientists and show that even the most successfulhave sometimes misrepresented findings or been influenced by theirown preconceived notions of religion, metaphysics, and the occult,or the personal beliefs of their mentors. Contrary to popularbelief, our greatest scientific thinkers approached their data witha combination of subjectivity and empiricism, and thus informallyachieved what is more formally accomplished by the modern Bayesianapproach to data analysis. Yet we are still taught that science is purely objective. Thisinnovative book dispels that myth using historical accounts andbiographical sketches of more than a dozen great scientists,including Aristotle, Galileo Galilei, Johannes Kepler, WilliamHarvey, Sir Isaac Newton, Antoine Levoisier, Alexander vonHumboldt, Michael Faraday, Charles Darwin, Louis Pasteur, GregorMendel, Sigmund Freud, Marie Curie, Robert Millikan, AlbertEinstein, Sir Cyril Burt, and Margaret Mead. Also included is adetailed treatment of the modern Bayesian approach to dataanalysis. Up-to-date references to the Bayesian theoretical andapplied literature, as well as reference lists of the primarysources of the principal works of all the scientists discussed,round out this comprehensive treatment of the subject. Readers will benefit from this cogent and enlightening view of thehistory of subjectivity in science and the authors' alternativevision of how the Bayesian approach should be used to further thecause of science and learning well into the twenty-first century.

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Genre : Mathematics
Author : S. James Press
Publisher : John Wiley & Sons
Release : 2012-01-20
File : 296 Pages
ISBN-13 : 9781118150627


Precedence Type Tests And Applications

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Full coverage of statistical techniques for developing and implementing precedence-type tests Precedence-Type Tests and Applications provides a comprehensive overview of theoretical and applied approaches to a variety of problems in which precedence-type test procedures can be used. The authors clearly demonstrate the effectiveness of these tests in life-testing situations designed for making quick and reliable decisions in the early stages of an experiment. Most of the text's examples use life-time data; however, theoretical properties are also discussed in the context of precedence testing. Monte Carlo studies are used to illustrate important results. Following the authors' careful step-by-step instructions and guidance, readers master the wide range of statistical techniques involved in the development and implementation of precedence-type tests. The book covers the foundations of precedence testing research from the early 1960s up to the most recent theory and applications, including the authors' current contributions to the field. The book features the following parts: * Part A deals with the original precedence test and some properties of precedence and related test procedures * Part B explores alternatives to precedence testing, including maximal precedence, weighted forms of precedence and maximal precedence, and Wilcoxon-type rank-sum precedence tests and their properties * Part C compares the extension of precedence, maximal precedence, and Wilcoxon-type rank-sum precedence tests to situations in which the sample arising from the life-testing experiment is progressively Type-II censored * Part D examines precedence-type tests in multi-sample situations and selection problems Tables are presented throughout the book to facilitate the application of the tests to practical problems. Helpful examples illustrate all of the precedence-type procedures, and an extensive bibliography enables readers to explore specialized topics in greater depth. This book is a recommended reference for researchers and practitioners in reliability and life-time data analysis, applied probabilists, and engineers. It also serves as a supplemental text for courses in nonparametric statistics and reliability.

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Genre : Mathematics
Author : Narayanaswamy Balakrishnan
Publisher : John Wiley & Sons
Release : 2006-05-26
File : 325 Pages
ISBN-13 : 9780470037836


Operational Risk

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Discover how to optimize business strategies from both qualitative and quantitative points of view Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors. Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts. Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science. In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features: * Ample exercises to further elucidate the concepts in the text * Definitive coverage of distribution functions and related concepts * Models for the size of losses * Models for frequency of loss * Aggregate loss modeling * Extreme value modeling * Dependency modeling using copulas * Statistical methods in model selection and calibration Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.

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Genre : Business & Economics
Author : Harry H. Panjer
Publisher : John Wiley & Sons
Release : 2006-07-28
File : 469 Pages
ISBN-13 : 9780471760894


Finding Groups In Data

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The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "Cluster analysis is the increasingly important and practical subject of finding groupings in data. The authors set out to write a book for the user who does not necessarily have an extensive background in mathematics. They succeed very well." —Mathematical Reviews "Finding Groups in Data [is] a clear, readable, and interesting presentation of a small number of clustering methods. In addition, the book introduced some interesting innovations of applied value to clustering literature." —Journal of Classification "This is a very good, easy-to-read, and practical book. It has many nice features and is highly recommended for students and practitioners in various fields of study." —Technometrics An introduction to the practical application of cluster analysis, this text presents a selection of methods that together can deal with most applications. These methods are chosen for their robustness, consistency, and general applicability. This book discusses various types of data, including interval-scaled and binary variables as well as similarity data, and explains how these can be transformed prior to clustering.

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Genre : Mathematics
Author : Leonard Kaufman
Publisher : John Wiley & Sons
Release : 2009-09-25
File : 368 Pages
ISBN-13 : 9780470317488


Clinical Trial Design

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A balanced treatment of the theories, methodologies, and design issues involved in clinical trials using statistical methods There has been enormous interest and development in Bayesian adaptive designs, especially for early phases of clinical trials. However, for phase III trials, frequentist methods still play a dominant role through controlling type I and type II errors in the hypothesis testing framework. From practical perspectives, Clinical Trial Design: Bayesian and Frequentist Adaptive Methods provides comprehensive coverage of both Bayesian and frequentist approaches to all phases of clinical trial design. Before underpinning various adaptive methods, the book establishes an overview of the fundamentals of clinical trials as well as a comparison of Bayesian and frequentist statistics. Recognizing that clinical trial design is one of the most important and useful skills in the pharmaceutical industry, this book provides detailed discussions on a variety of statistical designs, their properties, and operating characteristics for phase I, II, and III clinical trials as well as an introduction to phase IV trials. Many practical issues and challenges arising in clinical trials are addressed. Additional topics of coverage include: Risk and benefit analysis for toxicity and efficacy trade-offs Bayesian predictive probability trial monitoring Bayesian adaptive randomization Late onset toxicity and response Dose finding in drug combination trials Targeted therapy designs The author utilizes cutting-edge clinical trial designs and statistical methods that have been employed at the world's leading medical centers as well as in the pharmaceutical industry. The software used throughout the book is freely available on the book's related website, equipping readers with the necessary tools for designing clinical trials. Clinical Trial Design is an excellent book for courses on the topic at the graduate level. The book also serves as a valuable reference for statisticians and biostatisticians in the pharmaceutical industry as well as for researchers and practitioners who design, conduct, and monitor clinical trials in their everyday work.

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Genre : Medical
Author : Guosheng Yin
Publisher : John Wiley & Sons
Release : 2012-01-03
File : 368 Pages
ISBN-13 : 9780470581711


Latent Curve Models

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An effective technique for data analysis in the social sciences The recent explosion in longitudinal data in the social sciences highlights the need for this timely publication. Latent Curve Models: A Structural Equation Perspective provides an effective technique to analyze latent curve models (LCMs). This type of data features random intercepts and slopes that permit each case in a sample to have a different trajectory over time. Furthermore, researchers can include variables to predict the parameters governing these trajectories. The authors synthesize a vast amount of research and findings and, at the same time, provide original results. The book analyzes LCMs from the perspective of structural equation models (SEMs) with latent variables. While the authors discuss simple regression-based procedures that are useful in the early stages of LCMs, most of the presentation uses SEMs as a driving tool. This cutting-edge work includes some of the authors' recent work on the autoregressive latent trajectory model, suggests new models for method factors in multiple indicators, discusses repeated latent variable models, and establishes the identification of a variety of LCMs. This text has been thoroughly class-tested and makes extensive use of pedagogical tools to aid readers in mastering and applying LCMs quickly and easily to their own data sets. Key features include: Chapter introductions and summaries that provide a quick overview of highlights Empirical examples provided throughout that allow readers to test their newly found knowledge and discover practical applications Conclusions at the end of each chapter that stress the essential points that readers need to understand for advancement to more sophisticated topics Extensive footnoting that points the way to the primary literature for more information on particular topics With its emphasis on modeling and the use of numerous examples, this is an excellent book for graduate courses in latent trajectory models as well as a supplemental text for courses in structural modeling. This book is an excellent aid and reference for researchers in quantitative social and behavioral sciences who need to analyze longitudinal data.

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Genre : Mathematics
Author : Kenneth A. Bollen
Publisher : John Wiley & Sons
Release : 2005-12-23
File : 312 Pages
ISBN-13 : 9780471455929