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Statistical Tolerance Regions

Theory, Applications, and Computation

Thomas Mathew, Kalimuthu Krishnamoorthy

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John Wiley & Sons img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik


A modern and comprehensive treatment of tolerance intervals andregions The topic of tolerance intervals and tolerance regions hasundergone significant growth during recent years, with applicationsarising in various areas such as quality control, industry, andenvironmental monitoring. Statistical Tolerance Regionspresents the theoretical development of tolerance intervals andtolerance regions through computational algorithms and theillustration of numerous practical uses and examples. This is thefirst book of its kind to successfully balance theory and practice,providing a state-of-the-art treatment on tolerance intervals andtolerance regions. The book begins with the key definitions, concepts, andtechnical results that are essential for deriving toleranceintervals and tolerance regions. Subsequent chapters providein-depth coverage of key topics including: * Univariate normal distribution * Non-normal distributions * Univariate linear regression models * Nonparametric tolerance intervals * The one-way random model with balanced data * The multivariate normal distribution * The one-way random model with unbalanced data * The multivariate linear regression model * General mixed models * Bayesian tolerance intervals A final chapter contains coverage of miscellaneous topicsincluding tolerance limits for a ratio of normal random variables,sample size determination, reference limits and coverage intervals,tolerance intervals for binomial and Poisson distributions, andtolerance intervals based on censored samples. Theoreticalexplanations are accompanied by computational algorithms that canbe easily replicated by readers, and each chapter contains exercisesets for reinforcement of the presented material. Detailedappendices provide additional data sets and extensive tables ofunivariate and multivariate tolerance factors. Statistical Tolerance Regions is an ideal book forcourses on tolerance intervals at the graduate level. It is also avaluable reference and resource for applied statisticians,researchers, and practitioners in industry and pharmaceuticalcompanies.

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