Statistical Tolerance Regions
Theory, Applications, and Computation
(Sprache: Englisch)
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.
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Produktinformationen zu „Statistical Tolerance Regions “
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.
Klappentext zu „Statistical Tolerance Regions “
A 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 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
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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.
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- This valuable resource provides a thorough and detailed discussion of both univariate tolerance intervals and multivariate tolerance regions and is ideal for applied statisticians and statistical consultants.
- It was conceived based on the need to have a single source that brings together the recent developments as well as the earlier results on tolerance intervals and tolerance regions.
- This book discusses the theoretical derivation of tolerance intervals and tolerance regions in a wide variety of scenarios, along with applications and examples, and also illustrates the computational procedures.
- Real applications and data analysis are used to illustrate the results throughout the book.
- It was conceived based on the need to have a single source that brings together the recent developments as well as the earlier results on tolerance intervals and tolerance regions.
- This book discusses the theoretical derivation of tolerance intervals and tolerance regions in a wide variety of scenarios, along with applications and examples, and also illustrates the computational procedures.
- Real applications and data analysis are used to illustrate the results throughout the book.
Inhaltsverzeichnis zu „Statistical Tolerance Regions “
List of TablesPreface
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 š + 3/42
e)
4.4 One-Sided Tolerance Limits for N(¹; Ÿ2 š)
4.5 Two-Sided Tolerance Intervals for N(¹; Ÿ2 ? + Ÿ2 e)
4.6 Two-Sided Tolerance Intervals for N(¹; Ÿ2 š )
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; Ÿ2 ¿ + Ÿ2 e)
5.4 One-Sided Tolerance Limits for N(¹; Ÿ2 ¿)
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
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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
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
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Autoren-Porträt von Kalimuthu Krishnamoorthy, Thomas Mathew
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.
Bibliographische Angaben
- Autoren: Kalimuthu Krishnamoorthy , Thomas Mathew
- 2009, 1. Auflage, 496 Seiten, Maße: 16,1 x 24 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470380268
- ISBN-13: 9780470380260
- Erscheinungsdatum: 10.04.2009
Sprache:
Englisch
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