New estimation methods for the Grubbs model

Generalized fiducial inference for the precision of a measuring instrument without available replications on the observations is our main interest. In this paper, we study two new estimation procedures for the precision parameters, the product variability and the mean of the quantity of interest under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. The behavior of the point and interval estimators is assessed numerically through Monte Carlo simulation studies. Comparisons with two existing frequentist approaches and five existing Bayesian approaches are reported. Finally, a data set is analyzed using the proposed methodology.