Statistical Tolerance Regions / Wiley Series in Probability and Statistics (PDF)

A modern and comprehensive treatment of tolerance intervals and
regions

The topic of tolerance intervals and tolerance regions has
undergone significant growth during recent years, with applications
arising in various areas such as quality control, industry, and
environmental monitoring. Statistical Tolerance Regions
presents the theoretical development of tolerance intervals and
tolerance regions through computational algorithms and the
illustration of numerous practical uses and examples. This is the
first book of its kind to successfully balance theory and practice,
providing a state-of-the-art treatment on tolerance intervals and
tolerance regions.

The book begins with the key definitions, concepts, and
technical results that are essential for deriving tolerance
intervals and tolerance regions. Subsequent chapters provide
in-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 topics
including tolerance limits for a ratio of normal random variables,
sample size determination, reference limits and coverage intervals,
tolerance intervals for binomial and Poisson distributions, and
tolerance intervals based on censored samples. Theoretical
explanations are accompanied by computational algorithms that can
be easily replicated by readers, and each chapter contains exercise
sets for reinforcement of the presented material. Detailed
appendices provide additional data sets and extensive tables of
univariate and multivariate tolerance factors.

Statistical Tolerance Regions is an ideal book for
courses on tolerance intervals at the graduate level. It is also a
valuable reference and resource for applied statisticians,
researchers, and practitioners in industry and pharmaceutical
companies.