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Precedence-type tests and applications
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Hoboken, NJ : John Wiley & Sons, 2006
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9780471457206
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30000010158548 QA278.8 B344 2006 Open Access Book
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Summary

Summary

Full coverage of statistical techniques for developing and implementing precedence-type tests


Precedence-Type Tests and Applications provides a comprehensive overview of theoretical and applied approaches to a variety of problems in which precedence-type test procedures can be used. The authors clearly demonstrate the effectiveness of these tests in life-testing situations designed for making quick and reliable decisions in the early stages of an experiment. Most of the text's examples use life-time data; however, theoretical properties are also discussed in the context of precedence testing. Monte Carlo studies are used to illustrate important results.

Following the authors' careful step-by-step instructions and guidance, readers master the wide range of statistical techniques involved in the development and implementation of precedence-type tests. The book covers the foundations of precedence testing research from the early 1960s up to the most recent theory and applications, including the authors' current contributions to the field. The book features the following parts:
* Part A deals with the original precedence test and some properties of precedence and related test procedures
* Part B explores alternatives to precedence testing, including maximal precedence, weighted forms of precedence and maximal precedence, and Wilcoxon-type rank-sum precedence tests and their properties
* Part C compares the extension of precedence, maximal precedence, and Wilcoxon-type rank-sum precedence tests to situations in which the sample arising from the life-testing experiment is progressively Type-II censored
* Part D examines precedence-type tests in multi-sample situations and selection problems

Tables are presented throughout the book to facilitate the application of the tests to practical problems. Helpful examples illustrate all of the precedence-type procedures, and an extensive bibliography enables readers to explore specialized topics in greater depth.

This book is a recommended reference for researchers and practitioners in reliability and life-time data analysis, applied probabilists, and engineers. It also serves as a supplemental text for courses in nonparametric statistics and reliability.


Author Notes

N. Balakrishnan, PhD, is Professor of Mathematics and Statistics at McMaster University
H. K. Tony Ng, PhD, is Assistant Professor in the Department of Statistical Science at Southern Methodist University


Table of Contents

List of Tablesp. xiii
List of Figuresp. xxi
Prefacep. xxiii
1 Introductionp. 1
1.1 Problems of Interestp. 1
1.2 Special Considerationsp. 1
1.3 Special Form of Testingp. 2
1.4 Precedence Testsp. 2
1.5 Developmentsp. 3
2 Preliminariesp. 7
2.1 Life-Test Datap. 7
2.2 Order Statisticsp. 8
2.2.1 Joint Densities and Markovian Propertyp. 8
2.2.2 Marginal Densitiesp. 9
2.2.3 Momentsp. 11
2.2.4 Results for the Uniform Distributionp. 11
2.2.5 Results for the Exponential Distributionp. 13
2.3 Censored Datap. 15
2.3.1 Type-I Censoringp. 15
2.3.2 Type-II Censoringp. 16
2.4 Progressively Censored Datap. 17
2.4.1 General Propertiesp. 17
2.4.2 Results for the Uniform Distributionp. 19
2.4.3 Results for the Exponential Distributionp. 20
2.5 Some Useful Lifetime Distributionsp. 23
2.5.1 Exponential Distributionp. 23
2.5.2 Gamma Distributionp. 24
2.5.3 Weibull Distributionp. 25
2.5.4 Extreme Value Distributionp. 26
2.5.5 Lognormal Distributionp. 27
2.6 Wilcoxon's Rank-Sum Statisticp. 28
2.7 Randomized Testp. 29
3 Precedence Testp. 31
3.1 Introductionp. 31
3.2 Concept of Precedence Testp. 32
3.3 Exact Null Distributionp. 34
3.4 Exact Power Function Under Lehmann Alternativep. 35
3.5 Monte Carlo Simulation Under Location-Shift Alternativep. 39
3.6 Evaluation and Comparative Remarksp. 40
3.7 Properties of Precedence and Related Testsp. 52
3.7.1 Powerful Precedence Testsp. 52
3.7.2 Median Testsp. 53
3.7.3 Precedence-type Tests for Complete and Censored Datap. 54
3.7.4 Exceedance Statistics and Placement Statisticsp. 55
3.8 Illustrative Examplesp. 56
4 Maximal Precedence Testp. 61
4.1 Introductionp. 61
4.2 Exact Null Distributionp. 62
4.3 Exact Power Function Under Lehmann Alternativep. 66
4.4 Monte Carlo Simulation Under Location-Shift Alternativep. 72
4.5 Evaluation and Comparative Remarksp. 74
4.6 Illustrative Examplesp. 85
5 Weighted Precedence and Weighted Maximal Precedence Testsp. 87
5.1 Introductionp. 87
5.2 Test Statistics and Exact Null Distributionsp. 89
5.3 Exact Power Function Under Lehmann Alternativep. 90
5.4 Monte Carlo Simulation Under Location-Shift Alternativep. 93
5.5 Illustrative Examplesp. 94
6 Wilcoxon-type Rank-sum Precedence Testsp. 101
6.1 Introductionp. 101
6.2 Test Statistics and Exact Null Distributionsp. 102
6.2.1 Wilcoxon-type Rank-sum Precedence Test Statisticsp. 102
6.2.2 Null Distributionsp. 104
6.3 Large-Sample Approximation for the Null Distributionsp. 111
6.4 Exact Power Function Under Lehmann Alternativep. 113
6.5 Monte Carlo Simulation Under Location-Shift Alternativep. 126
6.6 Evaluation and Comparative Remarksp. 149
6.7 Illustrative Examplesp. 150
7 Extension to Progressive Censoringp. 153
7.1 Introductionp. 153
7.2 Test Statistics and Exact Null Distributionsp. 154
7.3 Exact Power Function Under Lehmann Alternativep. 156
7.4 Monte Carlo Simulation Under Location-Shift Alternativep. 163
7.5 Illustrative Examplep. 172
8 Generalization to k-Sample Situationp. 175
8.1 Introductionp. 175
8.2 Some Pertinent Problemsp. 176
8.3 Comparing Treatments with Controlp. 176
8.4 Comparison of Treatmentsp. 179
9 Selecting the Best Population Using a Test for Equality Based on Precedence Statisticp. 181
9.1 Introductionp. 181
9.2 Two-Sample Selection Problemp. 182
9.2.1 Equal Sample Size Situationp. 182
9.2.2 Unequal Sample Size Situationp. 184
9.2.3 Performance Under Lehmann Alternativep. 190
9.3 k-Sample Selection Problemp. 194
9.3.1 Selection Procedure and Null Distributionp. 194
9.3.2 Handling Tiesp. 197
9.4 Monte Carlo Simulation Under Location-Shiftp. 203
9.5 Evaluation and Comparative Remarksp. 226
9.6 Illustrative Examplesp. 226
10 Selecting the Best Population Using a Test for Equality Based on Minimal Wilcoxon Rank-sum Precedence Statisticp. 231
10.1 Introductionp. 231
10.2 Two-Sample Selection Problemp. 232
10.2.1 Equal Sample Size Situationp. 232
10.2.2 Unequal Sample Size Situationp. 234
10.2.3 Performance Under Lehmann Alternativep. 237
10.3 k-Sample Selection Problemp. 240
10.3.1 Selection Procedure and Null Distributionp. 240
10.3.2 Handling Tiesp. 244
10.4 Monte Carlo Simulation Under Location-Shiftp. 247
10.5 Evaluation and Comparative Remarksp. 248
10.6 Illustrative Examplesp. 265
Appendixp. 269
Bibliographyp. 275
Author Indexp. 283
Subject Indexp. 285