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| probability reliability and statistical methods: Probability, Reliability, and Statistical Methods in Engineering Design Achintya Haldar, Sankaran Mahadevan, 2000 Learn the tools to assess product reliability! Haldar and Mahadevan crystallize the research and experience of the last few decades into the most up-to-date book on risk-based design concepts in engineering available. The fundamentals of reliability and statistics necessary for risk-based engineering analysis and design are clearly presented. And with the help of many practical examples integrated throughout the text, the material is made very relevant to today's practice. Key Features * Covers all the fundamental concepts and mathematical skills needed to conduct reliability assessments. * Presents the most widely-used reliability assessment methods. * Concepts that are required for the implementation of risk-based design in practical problems are developed gradually. * Both risk-based and deterministic design concepts are included to show the transition from traditional to modern design practice. |
| probability reliability and statistical methods: Statistical Methods for Reliability Data William Q. Meeker, Luis A. Escobar, Francis G. Pascual, 2022-01-24 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. |
| probability reliability and statistical methods: System Reliability Theory Arnljot Høyland, Marvin Rausand, 2009-09-25 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. |
| probability reliability and statistical methods: Methods for Statistical Analysis of Reliability and Life Data Nancy R. Mann, Ray E. Schafer, Nozer D. Singpurwalla, 1974 |
| probability reliability and statistical methods: Mathematical and Statistical Methods in Reliability Bo Lindqvist, Kjell A. Doksum, 2003 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. |
| probability reliability and statistical methods: Statistical Methods in Software Engineering Nozer D. Singpurwalla, Simon P. Wilson, 2012-12-06 This preface pertains to three issues that we would like to bring to the attention of the readers: our objectives, our intended audience, and the nature of the material. We have in mind several objectives. The first is to establish a framework for dealing with uncertainties in software engineering, and for using quantitative measures for decision making in this context. The second is to bring into perspective the large body of work having statistical content that is relevant to software engineering, which may not have appeared in the traditional outlets devoted to it. Connected with this second objective is a desire to streamline and organize our own thinking and work in this area. Our third objective is to provide a platform that facilitates an interface between computer scientists and statisticians to address a class of problems in computer science. It appears that such an interface is necessary to provide the needed synergism for solving some difficult problems that the subject poses. Our final objective is to serve as an agent for stimulating more cross-disciplinary research in computer science and statistics. To what extent the material here will meet our objectives can only be assessed with the passage of time. Our intended audience is computer scientists, software engineers, and reliability analysts, who have some exposure to probability and statistics. Applied statisticians interested in reliability problems are also a segment of our intended audience. |
| probability reliability and statistical methods: Mathematical and Statistical Models and Methods in Reliability V.V. Rykov, N. Balakrishnan, M.S. Nikulin, 2010-11-02 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. |
| probability reliability and statistical methods: Probability Distributions Used in Reliability Engineering Andrew N O'Connor, 2011 The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering. |
| probability reliability and statistical methods: Statistical Methods Donna L. Mohr, 2010-08-17 Statistical Methods, Third Edition, provides students with a working introduction to statistical methods offering a wide range of applications that emphasize the quantitative skills useful across many academic disciplines. This text takes a classic approach that emphasizes concepts and techniques for working out problems and intepreting results. The book includes research projects, real-world case studies, numerous examples, and data exercises organized by level of difficulty. Students are required to be familiar with algebra. This updated edition includes new exercises applying different techniques and methods; new examples and datasets using current real-world data; new text organization to create a more natural connection between regression and the Analysis of the Variance; new material on generalized linear models; new expansion of nonparametric techniques; new student research projects; and new case studies for gathering, summarizing, and analyzing data. - Integrates the classical conceptual approach with modern day computerized data manipulation and computer applications - Accessibile to students who may not have a background in probability or calculus - Offers reader-friendly exposition, without sacrificing statistical rigor - Includes many new data sets in various applied fields such as Psychology, Education, Biostatistics, Agriculture, Economics |
| probability reliability and statistical methods: Probability and Statistics with Reliability, Queuing, and Computer Science Applications Kishor S. Trivedi, 2016-07-11 An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department. |
| probability reliability and statistical methods: Statistical Methods in Diagnostic Medicine Xiao-Hua Zhou, Donna K. McClish, Nancy A. Obuchowski, 2009-09-25 An important role of diagnostic medicine research is to estimate and compare the accuracies of diagnostic tests. This book provides a comprehensive account of statistical methods for design and analysis of diagnostic studies, including sample size calculations, estimation of the accuracy of a diagnostic test, comparison of accuracies of competing diagnostic tests, and regression analysis of diagnostic accuracy data. Discussing recently developed methods for correction of verification bias and imperfect reference bias, methods for analysis of clustered diagnostic accuracy data, and meta-analysis methods, Statistical Methods in Diagnostic Medicine explains: * Common measures of diagnostic accuracy and designs for diagnostic accuracy studies * Methods of estimation and hypothesis testing of the accuracy of diagnostic tests * Meta-analysis * Advanced analytic techniques-including methods for comparing correlated ROC curves in multi-reader studies, correcting verification bias, and correcting when an imperfect gold standard is used Thoroughly detailed with numerous applications and end-of-chapter problems as well as a related FTP site providing FORTRAN program listings, data sets, and instructional hints, Statistical Methods in Diagnostic Medicine is a valuable addition to the literature of the field, serving as a much-needed guide for both clinicians and advanced students. |
| probability reliability and statistical methods: Statistical Methods for the Reliability of Repairable Systems Steven E. Rigdon, Asit P. Basu, 2000-04-14 A unique, practical guide for industry professionals who need to improve product quality and reliability in repairable systems Owing to its vital role in product quality, reliability has been intensely studied in recent decades. Most of this research, however, addresses systems that are nonrepairable and therefore discarded upon failure. Statistical Methods for the Reliability of Repairable Systems fills the gap in the field, focusing exclusively on an important yet long-neglected area of reliability. Written by two highly recognized members of the reliability and statistics community, this new work offers a unique, systematic treatment of probabilistic models used for repairable systems as well as the statistical methods for analyzing data generated from them. Liberally supplemented with examples as well as exercises boasting real data, the book clearly explains the difference between repairable and nonrepairable systems and helps readers develop an understanding of stochastic point processes. Data analysis methods are discussed for both single and multiple systems and include graphical methods, point estimation, interval estimation, hypothesis tests, goodness-of-fit tests, and reliability prediction. Complete with extensive graphs, tables, and references, Statistical Methods for the Reliability of Repairable Systems is an excellent working resource for industry professionals involved in producing reliable systems and a handy reference for practitioners and researchers in the field. |
| probability reliability and statistical methods: Statistics and Probability with Applications for Engineers and Scientists Bhisham C Gupta, Irwin Guttman, 2014-03-06 Introducing the tools of statistics and probability from the ground up An understanding of statistical tools is essential for engineers and scientists who often need to deal with data analysis over the course of their work. Statistics and Probability with Applications for Engineers and Scientists walks readers through a wide range of popular statistical techniques, explaining step-by-step how to generate, analyze, and interpret data for diverse applications in engineering and the natural sciences. Unique among books of this kind, Statistics and Probability with Applications for Engineers and Scientists covers descriptive statistics first, then goes on to discuss the fundamentals of probability theory. Along with case studies, examples, and real-world data sets, the book incorporates clear instructions on how to use the statistical packages Minitab® and Microsoft® Office Excel® to analyze various data sets. The book also features: • Detailed discussions on sampling distributions, statistical estimation of population parameters, hypothesis testing, reliability theory, statistical quality control including Phase I and Phase II control charts, and process capability indices • A clear presentation of nonparametric methods and simple and multiple linear regression methods, as well as a brief discussion on logistic regression method • Comprehensive guidance on the design of experiments, including randomized block designs, one- and two-way layout designs, Latin square designs, random effects and mixed effects models, factorial and fractional factorial designs, and response surface methodology • A companion website containing data sets for Minitab and Microsoft Office Excel, as well as JMP ® routines and results Assuming no background in probability and statistics, Statistics and Probability with Applications for Engineers and Scientists features a unique, yet tried-and-true, approach that is ideal for all undergraduate students as well as statistical practitioners who analyze and illustrate real-world data in engineering and the natural sciences. |
| probability reliability and statistical methods: Statistical Intervals William Q. Meeker, Gerald J. Hahn, Luis A. Escobar, 2017-03-09 Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals. |
| probability reliability and statistical methods: Reliability Lawrence M. Leemis, 2009 An elementary introduction to the probabilistic models and statistical methods used by reliability engineers as applied to, for example, electrical or mechanical systems. Leemis offers explanations of how the mathematical models and results apply to engineering design and the analysis of lifetime data sets, with simple, supplementary proofs and derivations provided when necessary. Applications are drawn from a variety of disciplines. |
| probability reliability and statistical methods: Statistics and Probability in Forensic Anthropology Zuzana Obertová, Alistair Stewart, Cristina Cattaneo, 2020-07-28 Statistics and Probability in Forensic Anthropology provides a practical guide for forensic scientists, primarily anthropologists and pathologists, on how to design studies, how to choose and apply statistical approaches, and how to interpret statistical outcomes in the forensic practice. As with other forensic, medical and biological disciplines, statistics have become increasingly important in forensic anthropology and legal medicine, but there is not a single book, which specifically addresses the needs of forensic anthropologists in relation to the research undertaken in the field and the interpretation of research outcomes and case findings within the setting of legal proceedings. The book includes the application of both frequentist and Bayesian statistics in relation to topics relevant for the research and the interpretation of findings in forensic anthropology, as well as general chapters on study design and statistical approaches addressing measurement errors and reliability. Scientific terminology understandable to students and advanced practitioners of forensic anthropology, pathology and related disciplines is used throughout. Additionally, Statistics and Probability in Forensic Anthropology facilitates sufficient understanding of the statistical procedures and data interpretation based on statistical outcomes and models, which helps the reader confidently present their work within the forensic context, either in the form of case reports for legal purposes or as research publications for the scientific community. - Contains the application of both frequentist and Bayesian statistics in relation to topics relevant for forensic anthropology research and the interpretation of findings - Provides examples of study designs and their statistical solutions, partly following the layout of scientific manuscripts on common topics in the field - Includes scientific terminology understandable to students and advanced practitioners of forensic anthropology, legal medicine and related disciplines |
| probability reliability and statistical methods: System Reliability Theory Marvin Rausand, Arnljot Hoyland, 2003-12-05 A thoroughly updated and revised look at system reliability theory Since the first edition of this popular text was published nearly a decade ago, new standards have changed the focus of reliability engineering and introduced new concepts and terminology not previously addressed in the engineering literature. Consequently, the Second Edition of System Reliability Theory: Models, Statistical Methods, and Applications has been thoroughly rewritten and updated to meet current standards. To maximize its value as a pedagogical tool, the Second Edition features: Additional chapters on reliability of maintained systems and reliability assessment of safety-critical systems Discussion of basic assessment methods for operational availability and production regularity New concepts and terminology not covered in the first edition Revised sequencing of chapters for better pedagogical structure New problems, examples, and cases for a more applied focus An accompanying Web site with solutions, overheads, and supplementary information With its updated practical focus, incorporation of industry feedback, and many new examples based on real industry problems and data, the Second Edition of this important text should prove to be more useful than ever for students, instructors, and researchers alike. |
| probability reliability and statistical methods: Statistical Reliability Engineering Boris Gnedenko, Igor V. Pavlov, Igor A. Ushakov, 1999-05-03 Proven statistical reliability analysis methods-available for the first time to engineers in the West While probabilistic methods of system reliability analysis have reached an unparalleled degree of refinement, Russian engineers have concentrated on developing more advanced statistical methods. Over the past several decades, their efforts have yielded highly evolved statistical models that have proven to be especially valuable in the estimation of reliability based upon tests of individual units of systems. Now Statistical Reliability Engineering affords engineers a unique opportunity to learn both the theory behind and applications of those statistical methods. Written by three leading innovators in the field, Statistical Reliability Engineering: * Covers all mathematical models for statistical reliability analysis, including Bayesian estimation, accelerated testing, and Monte Carlo simulation * Focuses on the estimation of various measures of system reliability based on the testing of individual units * Contains new theoretical results available for the first time in print * Features numerous examples demonstrating practical applications of the theory presented Statistical Reliability Engineering is an important professional resource for reliability and design engineers, especially those in the telecommunications and electronics industries. It is also an excellent course text for advanced courses in reliability engineering. |
| probability reliability and statistical methods: Probability, Statistics, and Reliability for Engineers and Scientists Bilal M. Ayyub, Richard H. McCuen, 2016-04-19 In a technological society, virtually every engineer and scientist needs to be able to collect, analyze, interpret, and properly use vast arrays of data. This means acquiring a solid foundation in the methods of data analysis and synthesis. Understanding the theoretical aspects is important, but learning to properly apply the theory to real-world p |
| probability reliability and statistical methods: Statistical Methods for Communication Science Andrew F. Hayes, 2020-10-14 Statistical Methods for Communication Science is the only statistical methods volume currently available that focuses exclusively on statistics in communication research. Writing in a straightforward, personal style, author Andrew F. Hayes offers this accessible and thorough introduction to statistical methods, starting with the fundamentals of measurement and moving on to discuss such key topics as sampling procedures, probability, reliability, hypothesis testing, simple correlation and regression, and analyses of variance and covariance. Hayes takes readers through each topic with clear explanations and illustrations. He provides a multitude of examples, all set in the context of communication research, thus engaging readers directly and helping them to see the relevance and importance of statistics to the field of communication. Highlights of this text include: *thorough and balanced coverage of topics; *integration of classical methods with modern resampling approaches to inference; *consideration of practical, real world issues; *numerous examples and applications, all drawn from communication research; *up-to-date information, with examples justifying use of various techniques; and *downloadable resources with macros, data sets, figures, and additional materials. This unique book can be used as a stand-alone classroom text, a supplement to traditional research methods texts, or a useful reference manual. It will be invaluable to students, faculty, researchers, and practitioners in communication, and it will serve to advance the understanding and use of statistical methods throughout the discipline. |
| probability reliability and statistical methods: Case Studies in Reliability and Maintenance Wallace R. Blischke, D. N. Prabhakar Murthy, 2003-03-27 Introducing a groundbreaking companion book to a bestselling reliability text Reliability is one of the most important characteristics defining the quality of a product or system, both for the manufacturer and the purchaser. One achieves high reliability through careful monitoring of design, materials and other input, production, quality assurance efforts, ongoing maintenance, and a variety of related decisions and activities. All of these factors must be considered in determining the costs of production, purchase, and ownership of a product. Case Studies in Reliability and Maintenance serves as a valuable addition to the current literature on the subject of reliability by bridging the gap between theory and application. Conceived during the preparation of the editors' earlier work, Reliability: Modeling, Prediction, and Optimization (Wiley, 2000), this new volume features twenty-six actual case studies written by top experts in their fields, each illustrating exactly how reliability models are applied. A valuable companion book to Reliability: Modeling, Prediction, and Optimization, or any other textbook on the subject, the book features: * Case studies from fields such as aerospace, automotive, mining, electronics, power plants, dikes, computer software, weapons, photocopiers, industrial furnaces, granite building cladding, chemistry, and aircraft engines * A logical organization according to the life cycle of a product or system * A unified format of discussion enhanced by tools, techniques, and models for drawing one's own conclusions * Pertinent exercises for reinforcement of ideas Of equal value to both students of reliability theory as well as professionals in industry, Case Studies in Reliability and Maintenance should be required reading for anyone seeking to understand how reliability and maintenance issues can be addressed and resolved in the real world. |
| probability reliability and statistical methods: Statistical Methods for Reliability Data William Q. Meeker, Luis A. Escobar, Francis G. Pascual, 2021-12-29 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. |
| probability reliability and statistical methods: Statistical Methods for Quality Improvement Thomas P. Ryan, 2011-08-02 Praise for the Second Edition As a comprehensive statistics reference book for quality improvement, it certainly is one of the best books available. —Technometrics This new edition continues to provide the most current, proven statistical methods for quality control and quality improvement The use of quantitative methods offers numerous benefits in the fields of industry and business, both through identifying existing trouble spots and alerting management and technical personnel to potential problems. Statistical Methods for Quality Improvement, Third Edition guides readers through a broad range of tools and techniques that make it possible to quickly identify and resolve both current and potential trouble spots within almost any manufacturing or nonmanufacturing process. The book provides detailed coverage of the application of control charts, while also exploring critical topics such as regression, design of experiments, and Taguchi methods. In this new edition, the author continues to explain how to combine the many statistical methods explored in the book in order to optimize quality control and improvement. The book has been thoroughly revised and updated to reflect the latest research and practices in statistical methods and quality control, and new features include: Updated coverage of control charts, with newly added tools The latest research on the monitoring of linear profiles and other types of profiles Sections on generalized likelihood ratio charts and the effects of parameter estimation on the properties of CUSUM and EWMA procedures New discussions on design of experiments that include conditional effects and fraction of design space plots New material on Lean Six Sigma and Six Sigma programs and training Incorporating the latest software applications, the author has added coverage on how to use Minitab software to obtain probability limits for attribute charts. new exercises have been added throughout the book, allowing readers to put the latest statistical methods into practice. Updated references are also provided, shedding light on the current literature and providing resources for further study of the topic. Statistical Methods for Quality Improvement, Third Edition is an excellent book for courses on quality control and design of experiments at the upper-undergraduate and graduate levels. the book also serves as a valuable reference for practicing statisticians, engineers, and physical scientists interested in statistical quality improvement. |
| probability reliability and statistical methods: Statistical Analysis of Reliability Data Martin J. Crowder, Alan Kimber, T. Sweeting, R. Smith, 2017-11-13 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. |
| probability reliability and statistical methods: Robust Statistics Ricardo A. Maronna, R. Douglas Martin, Victor J. Yohai, Matías Salibián-Barrera, 2019-01-04 A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences. |
| probability reliability and statistical methods: Probability and Risk Analysis Igor Rychlik, Jesper Rydén, 2006-10-07 This text presents notions and ideas at the foundations of a statistical treatment of risks. The focus is on statistical applications within the field of engineering risk and safety analysis. Coverage includes Bayesian methods. Such knowledge facilitates the understanding of the influence of random phenomena and gives a deeper understanding of the role of probability in risk analysis. The text is written for students who have studied elementary undergraduate courses in engineering mathematics, perhaps including a minor course in statistics. This book differs from typical textbooks in its verbal approach to many explanations and examples. |
| probability reliability and statistical methods: Statistical Methods in Water Resources D.R. Helsel, R.M. Hirsch, 1993-03-03 Data on water quality and other environmental issues are being collected at an ever-increasing rate. In the past, however, the techniques used by scientists to interpret this data have not progressed as quickly. This is a book of modern statistical methods for analysis of practical problems in water quality and water resources.The last fifteen years have seen major advances in the fields of exploratory data analysis (EDA) and robust statistical methods. The 'real-life' characteristics of environmental data tend to drive analysis towards the use of these methods. These advances are presented in a practical and relevant format. Alternate methods are compared, highlighting the strengths and weaknesses of each as applied to environmental data. Techniques for trend analysis and dealing with water below the detection limit are topics covered, which are of great interest to consultants in water-quality and hydrology, scientists in state, provincial and federal water resources, and geological survey agencies.The practising water resources scientist will find the worked examples using actual field data from case studies of environmental problems, of real value. Exercises at the end of each chapter enable the mechanics of the methodological process to be fully understood, with data sets included on diskette for easy use. The result is a book that is both up-to-date and immediately relevant to ongoing work in the environmental and water sciences. |
| probability reliability and statistical methods: Accelerated Testing Wayne B. Nelson, 2009-09-25 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. . . . a goldmine of knowledge on accelerated life testing principles and practices . . . one of the very few capable of advancing the science of reliability. It definitely belongs in every bookshelf on engineering. –Dev G. Raheja, Quality and Reliability Engineering International . . . an impressive book. The width and number of topics covered, the practical data sets included, the obvious knowledge and understanding of the author and the extent of published materials reviewed combine to ensure that this will be a book used frequently. –Journal of the Royal Statistical Society A benchmark text in the field, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis offers engineers, scientists, and statisticians a reliable resource on the effective use of accelerated life testing to measure and improve product reliability. From simple data plots to advanced computer programs, the text features a wealth of practical applications and a clear, readable style that makes even complicated physical and statistical concepts uniquely accessible. A detailed index adds to its value as a reference source. |
| probability reliability and statistical methods: Reliability Wallace R. Blischke, D. N. Prabhakar Murthy, 2011-09-20 Bringing together business and engineering to reliability analysisWith manufactured products exploding in numbers and complexity,reliability studies play an increasingly critical role throughout aproduct's entire life cycle-from design to post-sale support.Reliability: Modeling, Prediction, and Optimization presents aremarkably broad framework for the analysis of the technical andcommercial aspects of product reliability, integrating concepts andmethodologies from such diverse areas as engineering, materialsscience, statistics, probability, operations research, andmanagement. Written in plain language by two highly respectedexperts in the field, this practical work provides engineers,operations managers, and applied statisticians with bothqualitative and quantitative tools for solving a variety ofcomplex, real-world reliability problems. A wealth of examples andcase studies accompanies: * Comprehensive coverage of assessment, prediction, and improvementat each stage of a product's life cycle * Clear explanations of modeling and analysis for hardware rangingfrom a single part to whole systems * Thorough coverage of test design and statistical analysis ofreliability data * A special chapter on software reliability * Coverage of effective management of reliability, product support,testing, pricing, and related topics * Lists of sources for technical information, data, and computerprograms * Hundreds of graphs, charts, and tables, as well as over 500references * PowerPoint slides are available from the Wiley editorialdepartment. |
| probability reliability and statistical methods: Robust Nonparametric Statistical Methods Thomas P. Hettmansperger, Joseph W. McKean, 1998 Offering an alternative to traditional statistical procedures which are based on least squares fitting, the authors cover such topics as one and two sample location models, linear models, and multivariate models. Both theory and applications are examined. |
| probability reliability and statistical methods: Modelling Uncertainty in Flood Forecasting Systems Shreedhar Maskey, 2004-05-15 Like all natural hazards, flooding is a complex and inherently uncertain phenomenon. Despite advances in developing flood forecasting models and techniques, the uncertainty in forecasts remains unavoidable. This uncertainty needs to be acknowledged, and uncertainty estimation in flood forecasting provides a rational basis for risk-based |
| probability reliability and statistical methods: A Mathematical Primer for Social Statistics John Fox, 2021-01-11 A Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic language of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a math camp or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods. |
| probability reliability and statistical methods: Reliability Engineering Joel A. Nachlas, 2005-04-12 Without proper reliability and maintenance planning, even the most efficient and seemingly cost-effective designs can incur enormous expenses due to repeated or catastrophic failure and subsequent search for the cause. Today’s engineering students face increasing pressure from employers, customers, and regulators to produce cost-efficient designs that are less prone to failure and that are safe and easy to use. An understanding of reliability principles and maintenance planning can help accomplish these conflicting goals. Presenting an integrated approach to reliability evaluation and maintenance planning, Reliability Engineering: Probabilistic Models and Maintenance Methods provides comprehensive coverage of the fundamental concepts of reliability theory, basic models, and various methods of analysis. It contains numerous examples and homework problems in each chapter. The first six chapters sequentially outline each basic concept of reliability theory, followed by two chapters on commonly used statistical methods for evaluating component reliability. The book concludes with five chapters on repairable systems and maintenance planning, a chapter devoted to special topics such as warranties, and appendices on numerical computation. With an accessible blend of mathematical rigor and readability, Reliability Engineering is the ideal introductory textbook for graduate students in reliability theory and engineering, repairable systems analysis, operations research methods, and applied random processes. |
| probability reliability and statistical methods: Applied Reliability Paul A. Tobias, David Trindade, 2011-08-26 Since the publication of the second edition of Applied Reliability in 1995, the ready availability of inexpensive, powerful statistical software has changed the way statisticians and engineers look at and analyze all kinds of data. Problems in reliability that were once difficult and time consuming even for experts can now be solved with a few well |
| probability reliability and statistical methods: Hilbert Space Methods in Probability and Statistical Inference Christopher G. Small, Don L. McLeish, 2011-09-15 Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples. |
| probability reliability and statistical methods: Reliability and Decision Making Richard E. Barlow, C.A. Claroti, Fabio Spizzichino, 1993-09-01 First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company. |
| probability reliability and statistical methods: Probability and Statistical Models Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu, 2010-08-26 With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. The material has been carefully selected to cover the basic concepts and techniques on each topic, making this an ideal introductory gateway to more advanced learning. With exercises and solutions to selected problems accompanying each chapter, this textbook is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics. |
| probability reliability and statistical methods: Reliability and Risk Nozer D. Singpurwalla, 2006-08-14 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. |
| probability reliability and statistical methods: Statistics, Probability, and Reliability for Civil and Environmental Engineers Nathabandu T. Kottegoda, Renzo Rosso, 1998-01 |
| probability reliability and statistical methods: An Introduction to Reliability and Maintainability Engineering Charles E. Ebeling, 2019-04-12 Many books on reliability focus on either modeling or statistical analysis and require an extensive background in probability and statistics. Continuing its tradition of excellence as an introductory text for those with limited formal education in the subject, this classroom-tested book introduces the necessary concepts in probability and statistics within the context of their application to reliability. The Third Edition adds brief discussions of the Anderson-Darling test, the Cox proportionate hazards model, the Accelerated Failure Time model, and Monte Carlo simulation. Over 80 new end-of-chapter exercises have been added, as well as solutions to all odd-numbered exercises. Moreover, Excel workbooks, available for download, save students from performing numerous tedious calculations and allow them to focus on reliability concepts. Ebeling has created an exceptional text that enables readers to learn how to analyze failure, repair data, and derive appropriate models for reliability and maintainability as well as apply those models to all levels of design. |
Probability - Wikipedia
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 …
Probability - Math is Fun
How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. When a coin is …
Probability - Formula, Calculating, Find, Theorems, Examples
Probability is all about how likely is an event to happen. For a random experiment with sample space S, the probability of happening of an event A is calculated by the probability formula n …
7.5: Basic Concepts of Probability - Mathematics LibreTexts
Define probability including impossible and certain events. Calculate basic theoretical probabilities. Calculate basic empirical probabilities. Distinguish among theoretical, empirical, …
Probability Definition in Math - BYJU'S
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they …
How To Calculate Probability - Math Steps, Examples & Questions
Free how to calculate probability math topic guide, including step-by-step examples, free practice questions, teaching tips and more!
What is Probability? Definition, Types, Formula, & Examples
Apr 7, 2025 · Probability is defined as the measure of how likely an event is to happen, usually expressed as a value between zero and one. A Probability of zero indicates that the event is …
Probability in Maths - GeeksforGeeks
May 16, 2025 · In this section, you will explore the fundamental concepts of probability, key formulas, conditional probability, and Bayes' Theorem. By the end, you'll have a clear …
Probability | Brilliant Math & Science Wiki
A probability is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to …
Probability - Definition, Formula, Types, Terms, Solved Problems
Jan 15, 2021 · Probability is defined as the possibility of an event to occur. The formula for Probability is given as the ratio of the number of favorable events to the total number of …
Probability - Wikipedia
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 …
Probability - Math is Fun
How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. When a coin is …
Probability - Formula, Calculating, Find, Theorems, Examples
Probability is all about how likely is an event to happen. For a random experiment with sample space S, the probability of happening of an event A is calculated by the probability formula n …
7.5: Basic Concepts of Probability - Mathematics LibreTexts
Define probability including impossible and certain events. Calculate basic theoretical probabilities. Calculate basic empirical probabilities. Distinguish among theoretical, empirical, …
Probability Definition in Math - BYJU'S
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they …
How To Calculate Probability - Math Steps, Examples & Questions
Free how to calculate probability math topic guide, including step-by-step examples, free practice questions, teaching tips and more!
What is Probability? Definition, Types, Formula, & Examples
Apr 7, 2025 · Probability is defined as the measure of how likely an event is to happen, usually expressed as a value between zero and one. A Probability of zero indicates that the event is …
Probability in Maths - GeeksforGeeks
May 16, 2025 · In this section, you will explore the fundamental concepts of probability, key formulas, conditional probability, and Bayes' Theorem. By the end, you'll have a clear …
Probability | Brilliant Math & Science Wiki
A probability is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to …
Probability - Definition, Formula, Types, Terms, Solved Problems
Jan 15, 2021 · Probability is defined as the possibility of an event to occur. The formula for Probability is given as the ratio of the number of favorable events to the total number of …
