A comparison between Rosenblatt's estimator and parametric density estimators for determining test limits

Because of measurement errors, test limits instead of specification limits are used for inspection to realize a prescribed bound on the consumer loss. Test limits based on the assumption of normality lead to severe violation of the prescribed bound when normality fails. While relaxing the assumption of normality, it is important to estimate the density of the inspected characteristic at the specification limit correctly. It is investigated whether larger parametric models provide a useful improvement. Simulations are carried out for several such models. It turns out that for estimating a density at a fixed point, the parametric estimators give improvements compared to application of the normal density. However, for small or moderate sample sizes Rosenblatt’s estimator is, in general, more accurate than the parametric density estimators