Krishnamoorthy / Mathew Statistical Tolerance Regions

Theory, Applications, and Computation
1. Auflage 2009
ISBN: 978-0-470-47389-4
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 496 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

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.

Autoren/Hrsg.

Krishnamoorthy, Kalimuthu

Mathew, Thomas

Inhaltsverzeichnis

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.
2.5 Simultaneous Tolerance Limits for Normal Populations.
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(µ, sigma²tau + sigma²taue).
4.4 One-Sided Tolerance Limits for N(µ, sigma²tau¨).
4.5 Two-Sided Tolerance Intervals for N(µ, sigma²tau + sigma²taue).
4.6 Two-Sided Tolerance Intervals for N(µ, sigma²tau¨).
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(µ, sigma²tau + sigma²e).
5.4 One-Sided Tolerance Limits for N(µ, sigma²tau).
5.5 Two-Sided Tolerance Intervals.
5.6 Exercises.
6 Some General Mixed Models.
6.1 Notations and Preliminaries.
6.2 Some Examples.
6.3 Tolerance Intervals in a General Setting.
6.4 A General Model with Two Variance Components.
6.5 A One-Way Random Model with Covariates and Unequal Variances.
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 beta-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.

Über Autor(innen)

K. Krishnamoorthy, PhD, is Professor in the Department ofMathematics at the University of Louisiana at Lafayette. He isAssociate Editor of Communications in Statistics and has publishednumerous journal articles in his areas of research interest, whichinclude tolerance regions, multivariate analysis, and statisticalcomputing.
Thomas Mathew, PhD, is Professor in the Department ofMathematics and Statistics at the University of Maryland, BaltimoreCounty. He currently focuses his research on tolerance regions,inference in linear mixed and random models, and bioequivalencetesting. A Fellow of the Institute of Mathematical Statistics andthe American Statistical Association, Dr. Mathew is the coauthor ofStatistical Tests for Mixed Linear Models, also published byWiley.