A comparison of estimators of the proportion nonconforming in univariate and multivariate normal samples

Maximum likelihood (ML) and minimum variance unbiased (MVU) estimators of the proportion nonconforming in univariate and bivariate normal random samples are compared for the case where the moments of the distribution are assumed to be unknown and each variable has lower and upper specification limits. Both types of estimator have skewed distributions when the proportion nonconforming and sample size are small, and the MVU estimator has a substantial probability of being zero in these situations. Using Pitman's closeness criterion, the ML estimators are nearly always superior to the MVU estimator for the cases considered. Using the MSE criterion, the MVU estimator is superior to the ML estimator when the distribution of the ML estimator is quite skewed. After transforming the estimators to symmetry, the ML estimator has smaller MSE than the MVU estimator.