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 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.

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