A basic measurement model for reference material preparation

The basic model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ x_{\text{CRM}} = x_{\text{char}} + \delta x_{\text{bb}} + \delta x_{\text{sts}} + \delta x_{\text{lts}} $$\end{document} in the ISO Guide 35 for the evaluation of uncertainty is reviewed. In the basic model, the authors of the Guide assume that the homogeneity and stability studies are designed in such a way that the values of the error terms are zero, but their uncertainties are not. Based on their assumption, it is shown that the basic model in the Guide requires output quantity xCRM to be employed as input quantities to define δxbb, δxsts, and δxlts, which results in circular reasoning on the value of CRM. In order to revise the basic model in the Guide, a proposed basic model Y = X is derived from the general model Y = X(1 + b′T) in the Guide as the special case of T = 0. The uncertainty evaluation for the proposed model is discussed. It is shown that it is not necessary to evaluate the uncertainty due to the between-bottle inhomogeneity ubb separately, when a single method is employed in the characterization. The ubb is shown to be one of the uncertainty components of the certified value xchar, because xchar is the mean value of at least 10 bottles.