Kalimuthu Krishnamoorthy, Thomas Mathew

Statistical Tolerance Regions

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 14538026000
• 1. Auflage
• Seitenzahl: 496
• Erscheinungstermin: 1. Mai 2009
• Englisch
• Abmessung: 240mm x 161mm x 31mm
• Gewicht: 775g
• ISBN-13: 9780470380260
• ISBN-10: 0470380268
• Artikelnr.: 26010051

Autorenporträt

K. Krishnamoorthy, PhD, is Professor in the Department of Mathematics at the University of Louisiana at Lafayette. He is Associate Editor of Communications in Statistics and has published numerous journal articles in his areas of research interest, which include tolerance regions, multivariate analysis, and statistical computing. Thomas Mathew, PhD, is Professor in the Department of Mathematics and Statistics at the University of Maryland, Baltimore County. He currently focuses his research on tolerance regions, inference in linear mixed and random models, and bioequivalence testing. A Fellow of the Institute of Mathematical Statistics and the American Statistical Association, Dr. Mathew is the coauthor of Statistical Tests for Mixed Linear Models, also published by Wiley.

Inhaltsangabe

List of Tables

Preface

1. Preliminaries

1.1 Introduction

1.2 Some Technical Results

1.3 The Modified Large Sample (MLS) Procedure

1.4 The Generalized P-value and Generalized Confidence Interval

1.5 Exercises

2. Univariate Normal Distribution

2.1 Introduction

2.2 One-Sided Tolerance Limits for a Normal Population

2.3 Two-Sided Tolerance Intervals

2.4 Tolerance Limits for X1 ¡ X2

2.6 Exercises

3. Univariate Linear Regression Model

3.1 Notations and Preliminaries

3.2 One-Sided Tolerance Intervals and Simultaneous Tolerance Intervals

3.3 Two-sided Tolerance Intervals and Simultaneous Tolerance Intervals

3.4 The Calibration Problem

3.5 Exercises

4. The One-Way Random Model With Balanced Data

4.1 Notations and Preliminaries

4.2 Two Examples

4.3 One-sided Tolerance Limits for N(¹; 3/42 ¨ + 3/42

e)

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

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

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

4.7 Exercises

5. The One-Way Random Model With Unbalanced Data

5.1 Notations and Preliminaries

5.2 Two Examples

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

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

5.5 Two-Sided Tolerance Intervals

5.6 Exercises

6. Some General Mixed Models

6.1 Some Examples

6.2 Tolerance Intervals in a General Setting

6.3 A General Model With Two Variance Components

6.4 A One-Way Random Model

6.5 Testing Individual Bioequivalence

6.6 Exercises

7. Some Non-normal Distributions

7.1 Introduction

7.2 Lognormal Distribution

7.3 Gamma Distribution

7.4 Two-parameter Exponential Distribution

7.5 Weibull Distribution

7.6 Exercises

8. Nonparametric Tolerance Intervals

8.1 Notations and Preliminaries

8.2 Order Statistics and Their Distributions

8.3 One-Sided Tolerance Limits and Exceedance Probabilities

8.4 Tolerance Intervals

8.5 Confidence Intervals for Population Quantiles

8.6 Sample Size Calculation

8.7 Nonparametric Multivariate Tolerance Regions

8.8 Exercises

9. The Multivariate Normal Distribution

9.1 Introduction

9.2 Notations and Preliminaries

9.3 Some Approximate Tolerance Factors

9.4 Methods Based on Monte Carlo Simulation

9.5 Simultaneous Tolerance Intervals

9.6 Tolerance Regions for Some Special Cases

9.7 Exercises

10. The Multivariate Linear Regression Model

10.1 Preliminaries

10.2 Approximations for the Tolerance Factor

10.3 Accuracy of the Approximate Tolerance Factors

10.4 Methods Based on Monte Carlo Simulation

10.5 Application to the Example

10.6 Multivariate Calibration

10.7 Exercises

11. Bayesian Tolerance Intervals

11.1 Notations and Preliminaries

11.2 The Univariate Normal Distribution

11.3 The One-Way Random Model With Balanced Data

11.4 Two Examples

11.5 Exercises

12. Miscellaneous Topics

12.1 Introduction

12.2 ¡Expectation Tolerance Regions

12.3 Tolerance Limits for a Ratio of Normal Random Variables

12.4 Sample Size Determination

12.5 Reference Limits and Coverage Intervals

12.6 Tolerance Intervals for Binomial and Poisson Distributions

12.7 Tolerance Intervals Based on Censored Samples

12.8 Exercises

Appendix A: Data Sets

Appendix B: Tables

References

Index