Full coverage of statistical techniques for developing and implementing precedence-type testsPrecedence-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 problemsTables 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(s): N. Balakrishnan, H. K. Tony Ng
Edition: 1
Publisher: Wiley-Interscience
Year: 2006
Language: English
Pages: 324
Contents......Page 9
1.2 SPECIAL CONSIDERATIONS......Page 27
1.4 PRECEDENCE TESTS......Page 28
1.5 DEVELOPMENTS......Page 29
2.1 LIFE-TEST DATA......Page 33
2.2.1 Joint Densities and Markovian Property......Page 34
2.2.2 Marginal Densities......Page 35
2.2.4 Results for the Uniform Distribution......Page 37
2.2.5 Results for the Exponential Distribution......Page 39
2.3.1 Type-I Censoring......Page 41
2.3.2 Type-II Censoring......Page 42
2.4.1 General Properties......Page 43
2.4.2 Results for the Uniform Distribution......Page 45
2.4.3 Results for the Exponential Distribution......Page 46
2.5.1 Exponential Distribution......Page 49
2.5.2 Gamma Distribution......Page 50
2.5.3 Weibull Distribution......Page 51
2.5.4 Extreme Value Distribution......Page 52
2.5.5 Lognormal Distribution......Page 53
2.6 WILCOXON’S RANK-SUM STATISTIC......Page 54
2.7 RANDOMIZED TEST......Page 55
3.1 INTRODUCTION......Page 57
3.2 CONCEPT OF PRECEDENCE TEST......Page 58
3.3 EXACT NULL DISTRIBUTION......Page 60
3.4 EXACT POWER FUNCTION UNDER LEHMANN ALTERNATIVE......Page 61
3.5 MONTE CARL0 SIMULATION UNDER LOCATION-SHIFT ALTERNATIVE......Page 65
3.6 EVALUATION AND COMPARATIVE REMARKS......Page 66
3.7.1 Powerful Precedence Tests......Page 78
3.7.2 Median Tests......Page 79
3.7.3 Precedence-type Tests for Complete and Censored Data......Page 80
3.7.4 Exceedance Statistics and Placement Statistics......Page 81
3.8 ILLUSTRATIVE EXAMPLES......Page 82
4.1 INTRODUCTION......Page 87
4.2 EXACT NULL DISTRIBUTION......Page 88
4.3 EXACT POWER FUNCTION UNDER LEHMANN ALTERNATIVE......Page 92
4.4 MONTE CARLO SIMULATION UNDER LOCATION- SHIFT ALTERNATIVE......Page 98
4.5 EVALUATION AND COMPARATIVE REMARKS......Page 100
4.6 ILLUSTRATIVE EXAMPLES......Page 111
5.1 INTRODUCTION......Page 113
5.2 TEST STATISTICS AND EXACT NULL DISTRIBUTIONS......Page 115
5.3 EXACT POWER FUNCTION UNDER LEHMANN ALTERNATIVE......Page 116
5.4 MONTE CARLO SIMULATION UNDER LOCATION- SHIFT ALTERNATIVE......Page 119
5.5 ILLUSTRATIVE EXAMPLES......Page 120
6.1 INTRODUCTION......Page 127
6.2.1 Wilcoxon-type Rank-sum Precedence Test Statistics......Page 128
6.2.2 Null Distributions......Page 130
6.3 LARGE-SAMPLE APPROXIMATION FOR THE NULL DISTRIBUTIONS......Page 137
6.4 EXACT POWER FUNCTION UNDER LEHMANN ALTERNATIVE......Page 139
6.5 MONTE CARLO SIMULATION UNDER LOCATION-SHIFT ALTERNATIVE......Page 152
6.6 EVALUATION AND COMPARATIVE REMARKS......Page 175
6.7 ILLUSTRATIVE EXAMPLES......Page 176
7.1 INTRODUCTION......Page 179
7.2 TEST STATISTICS AND EXACT NULL DISTRIBUTIONS......Page 180
7.3 EXACT POWER FUNCTION UNDER LEHMANN ALTERNATIVE......Page 182
7.4 MONTE CARLO SIMULATION UNDER LOCATION-SHIFT ALTERNATIVE......Page 189
7.5 ILLUSTRATIVE EXAMPLE......Page 198
8.1 INTRODUCTION......Page 201
8.3 COMPARING TREATMENTS WITH CONTROL......Page 202
8.4 COMPARISON OF TREATMENTS......Page 205
9.1 INTRODUCTION......Page 207
9.2.1 Equal Sample Size Situation......Page 208
9.2.2 Unequal Sample Size Situation......Page 210
9.2.3 Performance Under Lehmann Alternative......Page 216
9.3.1 Selection Procedure and Null Distribution......Page 220
9.3.2 Handling Ties......Page 223
9.4 MONTE CARLO SIMULATION UNDER LOCATION- SHIFT......Page 229
9.6 ILLUSTRATIVE EXAMPLES......Page 252
10.1 INTRODUCTION......Page 257
10.2.1 Equal Sample Size Situation......Page 258
10.2.2 Unequal Sample Size Situation......Page 260
10.2.3 Performance Under Lehmann Alternative......Page 263
10.3.1 Selection Procedure and Null Distribution......Page 266
10.3.2 Handling Ties......Page 270
10.4 MONTE CARL0 SIMULATION UNDER LOCATION-SHIFT......Page 273
10.5 EVALUATION AND COMPARATIVE REMARKS......Page 274
10.6 ILLUSTRATIVE EXAMPLES......Page 291
Appendix......Page 295
Bibliography......Page 301
Author Index......Page 309
Subject Index......Page 311
