Optimal estimator for uncertainty-based measurement quality control

Abstract

This paper presents an optimal estimator for uncertainty-based measurement quality control. The optimal estimator is developed based on an acceptance probability approach under a risk balance criterion. It yields a balance between the false acceptance and false rejection when the measurement quality index is equal to unity. This paper also presents a minimum mean absolute percentage error (MAPE) estimator and a minimum mean squared percentage error estimator based on the frequentist decision-theoretic approach. The mathematical formulations for computing the MAPE, relative bias error (RBE), relative precision error (RPE), and root mean squared percentage error (RMSPE) of the three presented estimators and five existing estimators are derived. The performance of these estimators are compared and evaluated in terms of the false acceptance/rejection probability, MAPE, RBE, RPE, and RMSPE. Among the eight estimators considered, the presented optimal estimator is the most meaningful and the best estimator from the measurement quality control perspective.