Confidence limits for conformance proportions in normal mixture models

Abstract

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.

Keywords:

• Generalized fiducial inference
• interval estimation
• latent variable
• Markov chain Monte Carlo
• quality control

Acknowledgments

The authors thank an associate editor and two anonymous reviewers for their insightful comments and constructive suggestions. The authors are grateful to Computer and Information Networking Center, National Taiwan University for the support of high-performance computing facilities.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Shin-Fu Tsai's research is supported in part by the Ministry of Science and Technology, Taiwan (grant number MOST 107-2118-M-002-002-MY2).