Confidence limits for conformance proportions in normal mixture models

Conformance proportions are important numerical indices for quality assessments. When the population is characterized by a normal mixture model, estimating conformance proportions can be a practical issue. To account for the inherent structure of normal mixture models, universal and individual conformance proportions are first defined for the purpose of evaluating the overall population and specific subpopulations of interest, respectively. On the basis of generalized fiducial quantities, a systematic method is then proposed in this paper to obtain confidence limits for the two classes of conformance proportions. The simulation results demonstrate that the proposed method can maintain the empirical coverage rate sufficiently close to the nominal level. In addition, two examples are given to illustrate the proposed method.