Unilateral Conformance Proportions in Balanced and Unbalanced Normal Random Effects Models

Abstract

Conformance proportion is the proportion of a performance characteristic of interest that falls within a prespecified acceptance region, which has been used in various applications. In this article, a simple closed-form interval estimation, based on Student’s t statistic, is proposed for unilateral conformance proportions in balanced and unbalanced random-effects models. Two real datasets are analyzed to illustrate the proposed method, whose performance is also evaluated through detailed simulation studies. The simulation results reveal that the empirical coverage probabilities for upper confidence limits of the method are sufficiently close to the nominal values, but those for lower confidence limits appear to be slightly less than the nominal level. Furthermore, a bootstrap-based calibration for both upper and lower confidence limits is provided to have empirical coverage probabilities closer to the nominal level. This article has supplementary material online.