Confidence Intervals and Bounds for a Ratio of Summed Expected Mean Squares

Abstract

To control manufacturing processes, it is necessary to measure product variability. A ratio that arises in camparing variance measures is δ = (k ₁θ₁, + k ₂θ₂)/(kθ₃ + k ₄θ₄), where 0₁, represents an expected mean square and k _i > 0 for i = 1, 2, 3, 4. Confidence bounds and intervals are require for making decisions based on δ. The Satterthwaite approximation is a popular method for constructing intervals on δ. This article presents and compares new methods for constructing approximate confidence intervals and bounds on δ. These new methods are shown to provide better approximations than the Satterthwaite method. A hypothesis test based on δ for a main effect in the balanced random three-factor crossed design is also presented.

KEY WORDS:

• Hypothesis testing
• Random-effects model
• Variance component