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This new book offers a guide to the theory and methods of progressive censoring. In many industrial experiments involving lifetimes of machines or units, experiments have to be terminated early. Progressive Censoring first introduces progressive sampling foundations, and then discusses various properties of progressive samples. The book points out the greater efficiency gained by using this scheme instead of classical right-censoring methods.
This book offers a thorough and updated guide to the theory and methods of progressive censoring, an area that has experienced tremendous growth over the last decade. The theory has developed quite nicely in some special cases having practical applications to reliability and quality. The Art of Progressive Censoring is a valuable reference for graduate students, researchers, and practitioners in applied statistics, quality control, life testing, and reliability. With its accessible style and concrete examples, the work may also be used as a textbook in an advanced undergraduate or a beginning graduate course on censoring or progressive censoring, as well as a supplementary textbook for a course on ordered data.
A method is offered for the effective estimation of the stationary waiting-time distribution of the GI/G/1 queue by a (possibly nonconvex) mixed exponential CDF. The approach relies on obtaining a generalized exponential mixture as an approximation for the distribution of the service times. This is done by the adaptation of a nonlinear optimization algorithm previously developed for the maximum-likelihood estimation of parameters from mixed Weibull distributions. The approach is particularly well-suited for obtaining the delay distribution beginning from raw interarrival and service-time data. (Author).
The class of probability functions expressed as linear (not necessarily convex) combinations of negative exponential densities is dense in the set of all distribution functions on the nonnegative reals. Because of this and resultant mathematical properties, such forms would appear to have excellent potential for wide application in stochastic modeling. This work documents the development and testing of a practical procedure for maximum-likelihood estimation for these generalized exponential mixtures. The algorithm offered for the problem is of the Jacobi type and guarantees that the result will provide a legitimate probability function of the prescribed type. Extensive testing has been performed and results are very favorable: convergence is rapid and the use of computer resources rather limited. (Author).
The types of articles most sought after by Naval Research Logistics fall into the following classes: (i) modeling and analysis of problems motivated by current real-world applications, (ii) exploratory modeling and analysis of problems motivated by potential future real-world applications, (iii) major methodological advances, and (iv) expository pieces of exceptional clarity. Areas represented include (but are not limited to) probability, statistics, simulation, optimization, game theory,scheduling, reliability, inventory, decision analysis, and combatmodels.
Understand and utilize the latest developments in Weibull inferential methods While the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. Using the Weibull Distribution: Reliability, Modeling, and Inference fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data. The author explains the use of the Weibull distribution and its statistical and probabilistic basis, providing a wealth of material that is not available in the current literature. The book begins by outlining the fundamental probability and statistical concepts that serve as a foundation for subsequent topics of coverage, including: • Optimum burn-in, age and block replacement, warranties and renewal theory • Exact inference in Weibull regression • Goodness of fit testing and distinguishing the Weibull from the lognormal • Inference for the Three Parameter Weibull Throughout the book, a wealth of real-world examples showcases the discussed topics and each chapter concludes with a set of exercises, allowing readers to test their understanding of the presented material. In addition, a related website features the author's own software for implementing the discussed analyses along with a set of modules written in Mathcad®, and additional graphical interface software for performing simulations. With its numerous hands-on examples, exercises, and software applications, Using the Weibull Distribution is an excellent book for courses on quality control and reliability engineering at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for engineers, scientists, and business analysts who gather and interpret data that follows the Weibull distribution
Censored sampling arises in a life testing experiment whenever the experimenter does not observe the failure times of all items placed on a life test. Progressive censoring scheme is useful in both industrial life testing applications and clinical settings; it allows the removal of surviving experimental units before the termination of the test. In this book, we obtain the maximum likelihood, and Bayes estimations for the parameter of the Burr-X model as well as the binomial parameter, based on progressive first-failure censoring with binomial removals. Bayes estimators under symmetric and asymmetric loss functions are obtained. Three special cases from this censoring scheme have been considered. Farther, we discuss the problem of predicting future record values and ordinary order statistics from Burr-X model based on progressively type-II censored with random removals, were the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval prediction. The maximum likelihood prediction both point and interval using "plug-in" procedure for future record values and ordinary order statistics are derived.