Statistical Methods for Reliability Data

Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information. Key Features: Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data. Describes methods of increasing importance with applications in areas such as environmental statistics and social science. Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples. Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data. This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.

Praise for the Third Edition “. . . an easy-to read introduction to survival analysis which covers the major concepts and techniques of the subject.” —Statistics in Medical Research Updated and expanded to reflect the latest developments, Statistical Methods for Survival Data Analysis, Fourth Edition continues to deliver a comprehensive introduction to the most commonly-used methods for analyzing survival data. Authored by a uniquely well-qualified author team, the Fourth Edition is a critically acclaimed guide to statistical methods with applications in clinical trials, epidemiology, areas of business, and the social sciences. The book features many real-world examples to illustrate applications within these various fields, although special consideration is given to the study of survival data in biomedical sciences. Emphasizing the latest research and providing the most up-to-date information regarding software applications in the field, Statistical Methods for Survival Data Analysis, Fourth Edition also includes: Marginal and random effect models for analyzing correlated censored or uncensored data Multiple types of two-sample and K-sample comparison analysis Updated treatment of parametric methods for regression model fitting with a new focus on accelerated failure time models Expanded coverage of the Cox proportional hazards model Exercises at the end of each chapter to deepen knowledge of the presented material Statistical Methods for Survival Data Analysis is an ideal text for upper-undergraduate and graduate-level courses on survival data analysis. The book is also an excellent resource for biomedical investigators, statisticians, and epidemiologists, as well as researchers in every field in which the analysis of survival data plays a role.

Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts – Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.

Praise for the First Edition «An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . .» -Choice «This is an important book, which will appeal to statisticians working on survival analysis problems.» -Biometrics «A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook.» -Statistics in Medicine The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data. Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, Second Edition provides broad coverage of the area without concentrating on any single field of application. Extensive illustrations and examples drawn from engineering and the biomedical sciences provide readers with a clear understanding of key concepts. New and expanded coverage in this edition includes: * Observation schemes for lifetime data * Multiple failure modes * Counting process-martingale tools * Both special lifetime data and general optimization software * Mixture models * Treatment of interval-censored and truncated data * Multivariate lifetimes and event history models * Resampling and simulation methodology

A practical guide for multivariate statistical techniques– now updated and revised In recent years, innovations in computer technology and statistical methodologies have dramatically altered the landscape of multivariate data analysis. This new edition of Methods for Statistical Data Analysis of Multivariate Observations explores current multivariate concepts and techniques while retaining the same practical focus of its predecessor. It integrates methods and data-based interpretations relevant to multivariate analysis in a way that addresses real-world problems arising in many areas of interest. Greatly revised and updated, this Second Edition provides helpful examples, graphical orientation, numerous illustrations, and an appendix detailing statistical software, including the S (or Splus) and SAS systems. It also offers * An expanded chapter on cluster analysis that covers advances in pattern recognition * New sections on inputs to clustering algorithms and aids for interpreting the results of cluster analysis * An exploration of some new techniques of summarization and exposure * New graphical methods for assessing the separations among the eigenvalues of a correlation matrix and for comparing sets of eigenvectors * Knowledge gained from advances in robust estimation and distributional models that are slightly broader than the multivariate normal This Second Edition is invaluable for graduate students, applied statisticians, engineers, and scientists wishing to use multivariate techniques in a variety of disciplines.

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. «This book, it must be said, lives up to the words on its advertising cover: 'Bridging the gap between introductory, descriptive approaches and highly advanced theoretical treatises, it provides a practical, intermediate level discussion of a variety of forecasting tools, and explains how they relate to one another, both in theory and practice.' It does just that!» -Journal of the Royal Statistical Society «A well-written work that deals with statistical methods and models that can be used to produce short-term forecasts, this book has wide-ranging applications. It could be used in the context of a study of regression, forecasting, and time series analysis by PhD students; or to support a concentration in quantitative methods for MBA students; or as a work in applied statistics for advanced undergraduates.» -Choice Statistical Methods for Forecasting is a comprehensive, readable treatment of statistical methods and models used to produce short-term forecasts. The interconnections between the forecasting models and methods are thoroughly explained, and the gap between theory and practice is successfully bridged. Special topics are discussed, such as transfer function modeling; Kalman filtering; state space models; Bayesian forecasting; and methods for forecast evaluation, comparison, and control. The book provides time series, autocorrelation, and partial autocorrelation plots, as well as examples and exercises using real data. Statistical Methods for Forecasting serves as an outstanding textbook for advanced undergraduate and graduate courses in statistics, business, engineering, and the social sciences, as well as a working reference for professionals in business, industry, and government.

The new edition adds a chapter on multiple linear regression in biomedical research, with sections including the multiple linear regressions model and least squares; the ANOVA table, parameter estimates, and confidence intervals; partial f-tests; polynomial regression; and analysis of covariance. * Organized by problem rather than method, so it guides readers to the correct technique for solving the problem at hand.

A new edition of the most comprehensive overview of statistical methods for environmental monitoring applications Thoroughly updated to provide current research findings, Statistical Methods for Groundwater Monitoring, Second Edition continues to provide a comprehensive overview and accessible treatment of the statistical methods that are useful in the analysis of environmental data. This new edition expands focus on statistical comparison to regulatory standards that are a vital part of assessment, compliance, and corrective action monitoring in the environmental sciences. The book explores quantitative concepts useful for surface water monitoring as well as soil and air monitoring applications while also maintaining a focus on the analysis of groundwater monitoring data in order to detect environmental impacts from a variety of sources, such as industrial activity and waste disposal. The authors introduce the statistical properties of alternative approaches, such as false positive and false negative rates, that are associated with each test and the factors related to these error rates. The Second Edition also features: An introduction to Intra-laboratory Calibration Curves and random-effects regression models for non-constant measurement variability Coverage of statistical prediction limits for a gamma-distributed random variable, with a focus on estimation and testing of parameters in environmental monitoring applications A unified treatment of censored data with the computation of statistical prediction, tolerance, and control limits Expanded coverage of statistical issues related to laboratory practice, such as detection and quantitation limits An updated chapter on regulatory issues that outlines common mistakes to avoid in groundwater monitoring applications as well as an introduction to the newest regulations for both hazardous and municipal solid waste facilities Each chapter provides a general overview of a problem, followed by statistical derivation of the solution and a relevant example complete with computational details that allow readers to perform routine application of the statistical results. Relevant issues are highlighted throughout, and recommendations are also provided for specific problems based on characteristics such as number of monitoring wells, number of constituents, distributional form of measurements, and detection frequency. Statistical Methods for Groundwater Monitoring, Second Edition is an excellent supplement to courses on environmental statistics at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the fields of biostatistics, engineering, and the environmental sciences who work with statistical methods in their everyday work.

A guide to achieving business successes through statistical methods Statistical methods are a key ingredient in providing data-based guidance to research and development as well as to manufacturing. Understanding the concepts and specific steps involved in each statistical method is critical for achieving consistent and on-target performance. Written by a recognized educator in the field, Statistical Methods for Six Sigma: In R&D and Manufacturing is specifically geared to engineers, scientists, technical managers, and other technical professionals in industry. Emphasizing practical learning, applications, and performance improvement, Dr. Joglekar?s text shows today?s industry professionals how to: Summarize and interpret data to make decisions Determine the amount of data to collect Compare product and process designs Build equations relating inputs and outputs Establish specifications and validate processes Reduce risk and cost-of-process control Quantify and reduce economic loss due to variability Estimate process capability and plan process improvements Identify key causes and their contributions to variability Analyze and improve measurement systems This long-awaited guide for students and professionals in research, development, quality, and manufacturing does not presume any prior knowledge of statistics. It covers a large number of useful statistical methods compactly, in a language and depth necessary to make successful applications. Statistical methods in this book include: variance components analysis, variance transmission analysis, risk-based control charts, capability and performance indices, quality planning, regression analysis, comparative experiments, descriptive statistics, sample size determination, confidence intervals, tolerance intervals, and measurement systems analysis. The book also contains a wealth of case studies and examples, and features a unique test to evaluate the reader?s understanding of the subject.