Assessment of the precision and bias of an online gauge using a single reference instrument
F Lombard, GJ Lyman

We consider the Grubbs estimation of the precision of an online gauge. Typically, this type of estimation involves independent results from two or more reference instruments (sampling and laboratory analysis operations). The properties of the estimator are then independent of the product variability. However, the use of more than one reference instrument entails significant additional costs.
The two-instrument Grubbs estimator, which is based on results from a gauge and a single reference instrument, has the disadvantage that its standard error is heavily dependent on the degree of product variability. We propose a new estimator that has a variance that is more or less independent of product variability. In fact, the variance is typically less than that of the Grubbs estimator based on the use of two reference instruments.
In order to function successfully, our methodology requires some prior knowledge of the extent of product variability and of gauge precision. In practice, such prior knowledge is often available and it is a weakness of the traditional two - and three-instrument Grubbs methods that no use is made of such knowledge. The efficacy and robustness of the new method is illustrated by Monte Carlo simulation.
Keywords: precision estimation, Grubbs estimator, Online analyser, ISO 15239, instrument variance.