Statistics for Industry and Technology – serie

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis, and related fields.

S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan’s influence and impact on these areas. Thematically organized, the chapters cover a broad range of topics from:- Inference - Ranking and Selection - Multiple Comparisons and Tests - Agreement Assessment - Reliability - Biostatistics Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.

This volume presents 32 invited chapters by researchers in this field of mathematics. The goal of the book is to bring together the work of theoreticians and applied researchers and provide a broad forum to share ideas and recent results. The collection describes and surveys theoretical developments and demonstrates some important applications in a variety of areas, including: applications to queueing theory; waiting time problems; applications to distribution theory; and applications to nonparametric statistics.

This new volume offers a throughout guide to the theory and methods of progressive censoring for practitioners and professionals in applied statistics, quality control, life testing and reliability testing. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early due to a variety of circumstances. Samples that arise from such experiments are called censored samples, and a new efficient alternative method is referred to as "progressive censoring" (where the removal of live units at time of failure is employed). This book first introduces progressive sampling foundations, then discusses various properties of progressive samples. It also describes how to make exact or approximate inferences for the difference statistical models with samples based on progressive censoring schemes. With many concrete examples, the book points out the greater efficiency gained by suing this scheme instead of classical right-censorship methods. With its accessible style and examples, the book should be an essential resource for progressive censoring methodology.Advanced students, practitioners, and professionals in applied statistics, reliability and life-testing research should find it a useful guide to understanding and using this new methodology in their work.

The present book is based on a course developed as partofthe large NSF-funded GatewayCoalitionInitiativeinEngineeringEducationwhichincludedCaseWest- ern Reserve University, Columbia University, Cooper Union, Drexel University, Florida International University, New Jersey Institute ofTechnology, Ohio State University, University ofPennsylvania, Polytechnic University, and Universityof South Carolina. The Coalition aimed to restructure the engineering curriculum by incorporating the latest technological innovations and tried to attract more and betterstudents to engineering and science. Draftsofthis textbookhave been used since 1992instatisticscoursestaughtatCWRU, IndianaUniversity, Bloomington, and at the universities in Gottingen, Germany, and Grenoble, France. Another purpose of this project was to develop a courseware that would take advantage ofthe Electronic Learning Environment created by CWRUnet-the all fiber-optic Case Western Reserve University computer network, and its ability to let students run Mathematica experiments and projects in their dormitory rooms, and interactpaperlessly with the instructor.Theoretically,onecould try togothroughthisbook withoutdoing Mathematica experimentsonthecomputer,butitwouldbelikeplayingChopin's Piano Concerto in E-minor, or Pink Floyd's The Wall, on an accordion. One would get an idea ofwhatthe tune was without everexperiencing the full richness andpowerofthe entire composition, and the whole ambience would be miscued.

This text presents advances in theory and methodology for this area of statistical research and application. The chapters contain broad coverage of theory and analytical and computational methods and techniques in four categories: introductory survey; discrete scan statistics; continuous scan statistics; and applications

This book is based on the papers presented at the International Conference 'Quality Improvement through Statistical Methods' in Cochin, India during December 28-31, 1996. The Conference was hosted by the Cochin University of Science and Technology, Cochin, India; and sponsored by the Institute for Improvement in Quality and Productivity (IIQP) at the University of Waterloo, Canada, the Statistics in Industry Committee of the International Statistical Institute (lSI) and by the Indian Statistical Institute. There has been an increased interest in Quality Improvement (QI) activities in many organizations during the last several years since the airing of the NBC television program, "If Japan can ... why can't we?" Implementation of QI meth­ ods requires statistical thinking and the utilization of statistical tools, thus there has been a renewed interest in statistical methods applicable to industry and technology. This revitalized enthusiasm has created worldwide discussions on Industrial Statistics Research and QI ideas at several international conferences in recent years. The purpose of this conference was to provide a forum for presenting and ex­ changing ideas in Statistical Methods and for enhancing the transference of such technologies to quality improvement efforts in various sectors. It also provided an opportunity for interaction between industrial practitioners and academia. It was intended that the exchange of experiences and ideas would foster new international collaborations in research and other technology transfers.

This volume consists of twenty-four papers selected by the editors from the sixty-one papers presented at the 1st International Conference on Mathemati­ cal Methods in Reliability held at the Politehnica University of Bucharest from 16 to 19 September 1997. The papers have been divided into three sections: statistical methods, probabilistic methods, and special techniques and appli­ cations. Of course, as with any classification, some papers could be as well assigned to other sections. Problems in reliability are encountered in items in everyday usage. Relia­ bility is an important feature of household appliances, cars, telephones, power supplies, and so on, whether viewed from the vantage of the producer or the consumer. Important decisions are based on the reliability of the product. Obtaining systems that perform adequately for a specified period of time in a given environment is an important goal for both government and industry. Hence study and use of reliability theory, which can be applied in the research, development, and production phases of a system to enable the user to evaluate and improve performance, is a worthwhile venture. If reliability theory is to be useful, it must be quantitative in nature, because reliability must be demonstra­ ble. Subsequently probability and statistics, among others, play an important part in its development.

This is a volume consisting of selected papers that were presented at the 3rd St. Petersburg Workshop on Simulation held at St. Petersburg, Russia, during June 28-July 3, 1998. The Workshop is a regular international event devoted to mathematical problems of simulation and applied statistics organized by the Department of Stochastic Simulation at St. Petersburg State University in cooperation with INFORMS College on Simulation (USA). Its main purpose is to exchange ideas between researchers from Russia and from the West as well as from other coun­ tries throughout the World. The 1st Workshop was held during May 24-28, 1994, and the 2nd workshop was held during June 18-21, 1996. The selected proceedings of the 2nd Workshop was published as a special issue of the Journal of Statistical Planning and Inference. Russian mathematical tradition has been formed by such genius as Tchebysh­ eff, Markov and Kolmogorov whose ideas have formed the basis for contempo­ rary probabilistic models. However, for many decades now, Russian scholars have been isolated from their colleagues in the West and as a result their mathe­ matical contributions have not been widely known. One of the primary reasons for these workshops is to bring the contributions of Russian scholars into lime­ light and we sincerely hope that this volume helps in this specific purpose.

Presents thirty-one chapters that provide a survey of models and methods for reliability analysis and applications in science, engineering, and technology. This book contains coverage of the developments and innovative techniques in a range of theoretical and numerical issues in the field of statistical and probabilistic methods in reliability.

This work provides an overview of semi-Markov processes and their applications in reliability. It contains examples which aid in the understanding of the theoretical notions and shows how to apply them to concrete physical situations including algorithmic simulations. Many examples of the concrete applications in reliability are given. The topics covered in the book include: processes associated to semi-Markov kernel for general and discrete state spaces; asymptotic theory of processes and of additive functionals; statistical estimation of semi-Markov kernel and of reliability function; and Monte Carlo simulation.

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

This volume is designed as a new source for modern topics dealing with wavelets, wavelet transforms, time-frequency signal analysis and other applications for future development of this new, important and useful subject for mathematics, science and engineering. Its main features include: A broad coverage of recent material on wavelet analysis, and time-frequency signal analysis and other applications that are not usually covered in other recent reference books. The material presented in this volume brings together a rich variety of ideas that blend most aspects of the subject mentioned above. This volume brings together a detailed account of major recent developments in wavelets, wavelet transforms and time-frequency signal analysis. This volume provides the reader with a thorough mathematical background and a wide variety of applications that are sufficient to do interdisciplinary collaborative research in applied mathematics. The book provides information that puts the reader at the forefront of the current resarch. An up-to-date bibliography is included at the end of each chapter to stimulate new interest in future study and research.

In this volume, several distinguished and active researchers will highlight some of the recent developments in statistical distribution theory, order statistics and their properties, and some inferential methods associated with them. The volume is classified into different parts according to the focus of the articles. Applications of the distributions and inferential procedures into survival analysis, reliability, quality control, and environmental problems will be highlighted. This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners, researchers and grad students in applied probability and statistics, reliability engineering, and biostatistics.

During the past three decades, the use of statistical methods in the health sciences has become quite common, and many sophisticated methods have been developed for specific applications and problems. Presented in this work are chapters covering a broad range of recent advances of statistical methods in the health sciences written by internationally renowned experts. The volume is thematically classified into different areas of the health sciences according to the particular focus of the chapters. Specific topics covered include stochastic models in cancer and AIDS studies, statistical methods in genome sequence analysis, bioequivalence studies, randomized clinical trial designs, survival analysis and applications, and statistical methods in quality-of-life. Some chapters are reviews of active research, while others highlight recent developments, new methods, and practical real-world data. This comprehensive reference text will serve the health sciences community, as well as practitioners, researchers, and graduate students in applied probability and biostatistics.

An outgrowth of the "International Conference on Statistical Models for Biomedical and Technical Systems," this book is comprised of contributions from renowned experts, demonstrating the significance of current research on theory, methods, and applications of the field.The contributions, which deal with the mathematical aspects of survival analysis and reliability as well as other topics, are a careful selection of invited and contributed chapters, reflecting recent developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics.The book will be useful to a broad interdisciplinary readership of researchers and practitioners in applied probability and statistics, industrial statistics, biomedicine, biostatistics, and engineering.

Enrique Castillo is a leading figure in several mathematical and engineering fields, having contributed seminal work in such areas as statistical modeling, extreme value analysis, multivariate distribution theory, Bayesian networks, neural networks, functional equations, artificial intelligence, linear algebra, optimization methods, numerical methods, reliability engineering, as well as sensitivity analysis and its applications. Organized to honor Castillo’s significant contributions, this volume is an outgrowth of the "International Conference on Mathematical and Statistical Modeling," and covers recent advances in the field.Applications to safety, reliability and life-testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented. The book is divided into nine major sections, which include distribution theory and applications, probability and statistics, order statistics and analysis, engineering modeling, extreme value theory, business and economics applications, statistical methods, applied mathematics, and discrete distributions.This comprehensive reference work will appeal to a diverse audience from the statistical, applied mathematics, engineering, and economics communities. Practitioners, researchers, and graduate students in mathematical and statistical modeling, optimization, and computing will benefit from this work.

Scan statistics is currently one of the most active and important areas of research in applied probability and statistics, having applications to a wide variety of fields: archaeology, astronomy, bioinformatics, biosurveillance, molecular biology, genetics, computer science, electrical engineering, geography, material sciences, physics, reconnaissance, reliability and quality control, telecommunication, and epidemiology.Filling a gap in the literature, this self-contained volume brings together a collection of selected chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics. The chapters are written by leading experts in the field of scan statistics. Key features include many current results and new directions for future research; challenging theoretical methodological research problems; presentation accessible to both statisticians and scientists from other disciplines where scan statistics are employed; emphasis on real-world applications to areas such as bioinformatics and biosurveillance; and extensive references to research articles, books, and relevant computer software.Scan Statistics is an excellent reference for graduate students and researchers in applied probability and statistics, as well as for scientists in biology, computer science, pharmaceutical science, medicine, geography, quality control, communications, and epidemiology. The work may also be used as a textbook for a graduate-level seminar on scan statistics.

An outgrowth of the 12th International Conference on Applied Stochastic Models and Data Analysis, this book is a collection of invited chapters presenting recent developments in the field of data analysis, with applications to reliability and inference, data mining, bioinformatics, lifetime data, and neural networks. Emphasized throughout the volume are new methods with the potential for solving real-world problems in various areas, including data mining and text mining, information theory and statistical applications, asymptotic behaviour of stochastic processes and random fields, bioinformatics and Markov chains, life table data, survival analysis, and risk in household insurance, neural networks and self-organizing maps, parametric and nonparametric statistics, and statistical theory and methods.Advances in Data Analysis is a useful reference for graduate students, researchers, and practitioners in statistics, mathematics, engineering, economics, social science, bioengineering, and bioscience.

This monograph offers a thorough and updated guide to the theory and methods of progressive censoring, an area that has experienced tremendous growth in recent years. Progressive censoring, originally proposed in the 1950s, is an efficient method of handling samples from industrial experiments involving lifetimes of units that have either failed or censored in a progressive fashion during the life test, with many practical applications to reliability and quality.Key topics and features:Data sets from the literature as well as newly simulated data sets are used to illustrate concepts throughout the textEmphasis on real-life applications to life testing, reliability, and quality controlDiscussion of parametric and nonparametric inferenceCoverage of experimental design with optimal progressive censoringThe Art of Progressive Censoring is a valuable reference for graduate students, researchers, and practitioners inapplied statistics, quality control, life testing, and reliability. With its accessible style and concrete examples, the work may also be used as a textbook in advanced undergraduate or beginning graduate courses on censoring or progressive censoring, as well as a supplementary textbook for a course on ordered data.

Contingency tables arise in diverse fields, including life sciences, education, social and political sciences, notably market research and opinion surveys. Their analysis plays an essential role in gaining insight into structures of the quantities under consideration and in supporting decision making.Combining both theory and applications, this book presents models and methods for the analysis of two- and multidimensional-contingency tables. The author uses a threefold approach, presenting fundamental models and related inference, highlighting their interpretational aspects, and demonstrating their practical usefulness.  Emphasis is on applications and methods of fitting models using standard statistical tools - such as SPSS, R, and BUGS - and on interpretation of the results. An excellent reference for advanced undergraduates, graduate students, and practitioners in statistics as well as biosciences, social sciences, education, and economics, the work may also be used as a textbook for a course on categorical data analysis. Prerequisites include basic background on statistical inference and knowledge of statistical software packages.

William Q. Meeker has made pioneering and phenomenal contributions to the general areaofreliabilityand,inparticular,tothetopicsofdegradationandacceleratedtesting. Hisresearchpublicationsandthenumerouscitationshehasreceivedoverthepastthree decades provide an ample testimony to this fact. Statistical methods have become critical in analyzing reliability and survival data. Highly reliable products have necessitated the development of accelerated testing and degradation models and their analyses. This volume has been put together in order to (i) review some of the recent advances on accelerated testing and degradation, (ii) highlight some new results and discuss their applications, and (iii) suggest possible directions for future research in these topics. With these speci?c goals in mind, many authors were invited to write a chapter for this volume. These authors are not only experts in lifetime data analysis, but also form a representative group from former students, colleagues, and other close professional associates of William Meeker. All contributions have been peer reviewed and organized into 26 chapters. For the convenience of readers, the volume has been divided into the following six parts: • Review, Tutorials, and Perspective • Shock Models • Degradation Models • Reliability Estimation and ALT • Survival Function Estimation • Competing Risk and Chaotic Systems Itneedstobeemphasizedherethatthisvolumeisnotaproceedings,butacarefully anddeliberatelyplannedvolumecomprisingchaptersconsistentwiththeeditorialgoals and purposes mentioned above. Our thanks go to all the authors who have contributed to this volume. Thanks are also due to Mrs. Debbie Iscoe for the excellent typesetting of the entire volume.SpecialthanksgotoMs.ReginaGorenshteynandMr.TomGrasso(Editor,Birkh¨ auser, Boston) for their interest and support for this project.

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.

Quantile-Based Reliability Analysis presents a novel approach to reliability theory using quantile functions in contrast to the traditional approach based on distribution functions. Quantile functions and distribution functions are mathematically equivalent ways to define a probability distribution. However, quantile functions have several advantages over distribution functions. First, many data sets with non-elementary distribution functions can be modeled by quantile functions with simple forms. Second, most quantile functions approximate many of the standard models in reliability analysis quite well. Consequently, if physical conditions do not suggest a plausible model, an arbitrary quantile function will be a good first approximation. Finally, the inference procedures for quantile models need less information and are more robust to outliers. Quantile-Based Reliability Analysis’s innovative methodology is laid out in a well-organized sequence of topics, including: ·       Definitions and properties of reliability concepts in terms of quantile functions;·       Ageing concepts and their interrelationships;·       Total time on test transforms;·       L-moments of residual life;·       Score and tail exponent functions and relevant applications;·       Modeling problems and stochastic orders connecting quantile-based reliability functions.  An ideal text for advanced undergraduate and graduate courses in reliability and statistics, Quantile-Based Reliability Analysis also contains many unique topics for study and research in survival analysis, engineering, economics, and the medical sciences. In addition, its illuminating discussion of the general theory of quantile functions is germane to many contexts involving statistical analysis.

This introductory textbook is designed for a one-semester course on queueing theory that does not require a course on stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering. This edition includes additional topics in methodology and applications.Key features:• An introductory chapter including a historical account of the growth of queueing theory in more than 100 years.• A modeling-based approach with emphasis on identification of models • Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics.• A chapter on matrix-analytic method asan alternative to the traditional methods of analysis of queueing systems.• A comprehensive treatment of statistical inference for queueing systems.• Modeling exercises and review exercises when appropriate. The second edition of An Introduction of Queueing Theory may be used as a textbook by first-year graduate students in fields such as computer science, operations research, industrial and systems engineering, as well as related fields such as manufacturing and communications engineering. Upper-level undergraduate students in mathematics, statistics, and engineering may also use the book in an introductory course on queueing theory. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research."...This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books." - Assam Statistical Review of the first edition

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis, and related fields.

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches.