Statistical Tolerance Regions: Theory, Applications, and Computation

by Kalimuthu Krishnamoorthy (Univ. of Louisiana at Lafayette ); Thomas Mathew (Univ. of Maryland Baltimore County, USA )

• ISBN13: 9780470473894
• ISBN10: 0470473894
• Format: eBook
• Copyright: 2009-05-01
• Publisher: Wiley

Summary

Statistical Tolerance RegionsTheory, Applications, and ComputationA modern and comprehensive treatment of tolerance intervals and regionsThe 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 distributionNon-normal distributionsUnivariate linear regression modelsNonparametric tolerance intervalsThe one-way random model with balanced dataThe multivariate normal distributionThe one-way random model with unbalanced dataThe multivariate linear regression modelGeneral mixed modelsBayesian tolerance intervalsA 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.

Table of Contents

List of Tables

Preface

Preliminaries

Introduction

Some Technical Results

The Modified Large Sample (MLS) Procedure

The Generalized P-value and Generalized Confidence Interval

Exercises

Univariate Normal Distribution

Introduction

One-Sided Tolerance Limits for a Normal Population

Two-Sided Tolerance Intervals

Tolerance Limits for X1 í X2

Exercises

Univariate Linear Regression Model

Notations and Preliminaries

One-Sided Tolerance Intervals and Simultaneous Tolerance Intervals

Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals

The Calibration Problem

Exercises

The One-Way Random Model With Balanced Data

Notations and Preliminaries

Two Examples

One-sided Tolerance Limits for N(¹; ¾2 ¿ + ¾2te)

One-Sided Tolerance Limits for N(¹; ¾2 ¿)

Two-Sided Tolerance Intervals for N(¹; ¾2 ? + ¾2 e)

Two-Sided Tolerance Intervals for N(¹; ¾2 ¿ )

Exercises

The One-Way Random Model With Unbalanced Data

Notations and Preliminaries

Two Examples

One-Sided Tolerance Limits for N(¹; ¾2 ¿ + ¾2 e)

One-Sided Tolerance Limits for N(¹; ¾2 ¿)

Two-Sided Tolerance Intervals

Exercises

Some General Mixed Models

Some Examples

Tolerance Intervals in a General Setting

A General Model With Two Variance Components

A One-Way Random Model

Testing Individual Bioequivalence

Exercises

Some Non-normal Distributions

Introduction

Lognormal Distribution

Gamma Distribution

Two-parameter Exponential Distribution

Weibull Distribution

Exercises

Nonparametric Tolerance Intervals

Notations and Preliminaries

Order Statistics and Their Distributions

One-Sided Tolerance Limits and Exceedance Probabilities

Tolerance Intervals

Confidence Intervals for Population Quantiles

Sample Size Calculation

Nonparametric Multivariate Tolerance Regions

Exercises

The Multivariate Normal Distribution

Introduction

Notations and Preliminaries

Some Approximate Tolerance Factors

Methods Based on Monte Carlo Simulation

Simultaneous Tolerance Intervals

Tolerance Regions for Some Special Cases

Exercises

The Multivariate Linear Regression Model

Preliminaries

Approximations for the Tolerance Factor

Accuracy of the Approximate Tolerance Factors

Methods Based on Monte Carlo Simulation

Application to the Example

Multivariate Calibration

Exercises

Bayesian Tolerance Intervals

Notations and Preliminaries

The Univariate Normal Distribution

The One-Way Random Model With Balanced Data

Two Examples

Exercises

Miscellaneous Topics

Introduction

íExpectation Tolerance Regions

Tolerance Limits for a Ratio of Normal Random Variables

Sample Size Determination

Reference Limits and Coverage Intervals

Tolerance Intervals for Binomial and Poisson Distributions

Tolerance Intervals Based on Censored Samples

Exercises

Data Sets

Tables

References

Index

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