This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and its utility is illustrated through practical applications to a variety of fields, including the reliability of engineering systems, hypothesis testing, quality control, and continuity measurement in the health care sector.
A rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics.
Reliability Analysis and Plans for Successive Testing: Start-up Demonstration Tests and Applications discusses all past and recent developments on start-up demonstration tests in the context of current numerical and illustrative examples to clarify available methods for distribution theorists and applied mathematicians dealing with control problems. Throughout the book, the authors focus on the panorama of open problems and issues of further interest. As contemporary manufacturers face tremendous commercial pressures to assemble works of high reliability, defined as 'the probability of the product performing its role under the stated conditions and over a specified period of time', this book helps address testing issues. - Unites the tools and methodologies of applied statistics and stochastic modeling to aid the determination of device reliability for better performing consumer goods - Clearly articulates how successive testing methods can be used in practice - Comments not only on distribution sequences closed, but also on open problems and issues of further interest for researchers
This book explores nonparametric statistical process control. It provides an up-to-date overview of nonparametric Shewhart-type univariate control charts, and reviews the recent literature on nonparametric charts, particularly multivariate schemes. Further, it discusses observations tied to the monitored population quantile, focusing on the Shewhart Sign chart. The book also addresses the issue of practically assuming the normality and the independence when a process is statistically monitored, and examines in detail change-point analysis-based distribution-free control charts designed for Phase I applications. Moreover, it introduces six distribution-free EWMA schemes for simultaneously monitoring the location and scale parameters of a univariate continuous process, and establishes two nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. Lastly, the book proposes novel and effective method for early disease detection.
This volume consists of a collection of research articles on classical and emerging Statistical Paradigms — parametric, non-parametric and semi-parametric, frequentist and Bayesian — encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. For advances in theory, the topics include: Bayesian Inference, Directional Data Analysis, Distribution Theory, Econometrics and Multiple Testing Procedures. The areas in emerging applications include: Bioinformatics, Factorial Experiments and Linear Models, Hotspot Geoinformatics and Reliability.
A unique approach to understanding the foundations of statistical quality control with a focus on the latest developments in nonparametric control charting methodologies Statistical Process Control (SPC) methods have a long and successful history and have revolutionized many facets of industrial production around the world. This book addresses recent developments in statistical process control bringing the modern use of computers and simulations along with theory within the reach of both the researchers and practitioners. The emphasis is on the burgeoning field of nonparametric SPC (NSPC) and the many new methodologies developed by researchers worldwide that are revolutionizing SPC. Over the last several years research in SPC, particularly on control charts, has seen phenomenal growth. Control charts are no longer confined to manufacturing and are now applied for process control and monitoring in a wide array of applications, from education, to environmental monitoring, to disease mapping, to crime prevention. This book addresses quality control methodology, especially control charts, from a statistician’s viewpoint, striking a careful balance between theory and practice. Although the focus is on the newer nonparametric control charts, the reader is first introduced to the main classes of the parametric control charts and the associated theory, so that the proper foundational background can be laid. Reviews basic SPC theory and terminology, the different types of control charts, control chart design, sample size, sampling frequency, control limits, and more Focuses on the distribution-free (nonparametric) charts for the cases in which the underlying process distribution is unknown Provides guidance on control chart selection, choosing control limits and other quality related matters, along with all relevant formulas and tables Uses computer simulations and graphics to illustrate concepts and explore the latest research in SPC Offering a uniquely balanced presentation of both theory and practice, Nonparametric Methods for Statistical Quality Control is a vital resource for students, interested practitioners, researchers, and anyone with an appropriate background in statistics interested in learning about the foundations of SPC and latest developments in NSPC.
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Heterogeneous Networking for Quality, Reliability, Security and Robustness, QShine 2010. The 37 revised full papers presented along with 7 papers from the allocated Dedicated Short Range Communications Workshop, DSRC 2010, were carefully selected from numerous submissions. Conference papers are organized into 9 technical sessions, covering the topics of cognitive radio networks, security, resource allocation, wireless protocols and algorithms, advanced networking systems, sensor networks, scheduling and optimization, routing protocols, multimedia and stream processing. Workshop papers are organized into two sessions: DSRC networks and DSRC security.
This unified volume 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. The book is a useful reference for graduate students, researchers, and practitioners in statistics, mathematics, engineering, economics, social science, bioengineering, and bioscience.
This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.
The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis tics has also found exciting applications in diverse disciplines such as archaeol ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.
