Generalized p Values and Confidence Intervals for Variance Components: Applications to Army Test and Evaluation

Various mixed models that are relevant for analyzing Army test data are described, along with several hypothesis testing and interval estimation problems. The problems come up in the context of investigating gun tube accuracy of an M1 Series tank; in particular, for the study of tube-to-tube dispers...

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Bibliographic Details
Published in:Technometrics 2005-08, Vol.47 (3), p.312-322
Main Authors: Mathew, Thomas, Webb, David W
Format: Article
Language:English
Subjects:
Accuracy
Ammunition
Armored vehicles
Confidence interval
Confidence intervals
Exact sciences and technology
Firearms
Firing occasion
Generalized confidence interval
Generalized p value
Guns
Hypothesis testing
Mathematical intervals
Mathematical models
Mathematics
Multivariate analysis
Musical intervals
Nested effect
P values
Probability and statistics
Random variables
Research and development laboratories
Satterthwaite approximation
Sciences and techniques of general use
Statistical variance
Statistics
Tests
Tube-to-tube variability
Variance analysis
Variance component
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Summary:Various mixed models that are relevant for analyzing Army test data are described, along with several hypothesis testing and interval estimation problems. The problems come up in the context of investigating gun tube accuracy of an M1 Series tank; in particular, for the study of tube-to-tube dispersion. Factors that affect tube-to-tube variability might include the tanks, ammunition lot, ammunition temperature, firing occasions, and so on. Some of these are fixed factors, and others are random factors. The inference problems that arise in the study of tube-to-tube dispersion are somewhat different from those usually encountered in typical ANOVA situations. A unified approach to solving these problems is presented using the concepts of generalized p values and generalized confidence intervals. The performance of the resulting tests and confidence intervals is numerically investigated and is found to be quite satisfactory. Analysis of some Army test data is presented to illustrate the results.
ISSN:0040-1706
1537-2723
DOI:10.1198/004017005000000265