Estimation for Conformance Proportions in a Normal Variance Components Model

Abstract

Two approaches are proposed for constructing one- and two-sided confidence limits for conformance proportions in a normal variance components model. One approach is based on the concepts of a generalized pivotal quantity, and the other is developed using the modified large-sample method for estimating linear combinations of variance components. The performance of the proposed methods is evaluated through detailed simulation studies. The results reveal that the empirical coverage probabilities for both methods are close to the claimed values and hence their performance is judged to be satisfactory. Nonetheless, the modified large—sample-based method might be recommended in practical applications due to its slightly better performance and computational ease. The framework established in this article can be applied to conformance proportion questions arising in arbitrary balanced mixed linear-model situations. The methods are illustrated using three real datasets. Finally, a bootstrap calibration approach is adopted to have empirical coverage probabilities sufficiently close to the nominal level for the proposed methods.

• Generalized Pivotal Quantity
• Modified Large Sample
• Parametric Bootstrap
• Process-Capability Index
• Tolerance Interval

Additional information

Notes on contributors

Hsin-I Lee

Ms. Lee is a PhD candidate in the Division of Biometry, Institute of Agronomy. Her email address is [email protected].

Chen-Tuo Liao

Dr. Liao is a Professor in the Division of Biometry, Institute of Agronomy. His email address is [email protected].