Statistical tolerance regions : theory, applications, and computation
Krishnamoorthy, K. (Kalimuthu)
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Preface xvii
1 Preliminaries 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 One-sided Tolerance Intervals . . . . . . . . . . . . . . . . 2
1.1.2 Tolerance Intervals . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Some Technical Results . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 The Modified Large Sample (MLS) Procedure . . . . . . . . . . . 11
1.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 GPQs for a Location-Scale Family . . . . . . . . . . . . . 16
1.4.3 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.1.3 Survival Probability and Stress-Strength Reliability . . . 5
1.4 The Generalized P-value and Generalized Confidence Interval . . 13
2 Univariate Normal Distribution
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 One-sided Tolerance Limits for a Normal Population . . . . . . .
2.3 Two-sided Tolerance Intervals . . . . . . . . . . . . . . . . . . . .
2.3.1 Tolerance Intervals . . . . . . . . . . . . . . . . . . . . . .
2.3.2
2.3.3
Equal-Tailed Tolerance Intervals for a Normal Distribution
Simultaneous Hypothesis Testing about Normal Quantiles
Exact One-sided Tolerance Limits for the Distribution of
XI - X2 When the Variance Ratio Is Known . . . . . . .
2.4 Tolerance Limits for X I - X2 . . . . . . . . . . . . . . . . . . . .