Forming a comparison reference value from different distributions of belief

If measurement uncertainty is to be expressed by forming a distribution of belief for the measurand then this should be reflected in the theory underlying the analysis of interlaboratory comparison data. This paper presents a corresponding method for the calculation of a reference value in a comparison where each laboratory independently assigns a probability density function, fi(x), to the value X of a stable artefact. Straightforward argument shows that a consensus density function for X can be taken as , assuming that the densities of the n laboratories are reliable and mutually consistent. A method is also presented for examining this consistency. The result f(x) is a special case of a consensus in the statistical literature called the logarithmic opinion pool. The key comparison reference value might be taken as the mean, median or mode of f(x).The method developed does not explicitly involve laboratory biases (offsets), which are important features of most methods for comparison analysis published recently and which are relevant to the calculation of degrees of equivalence. The belief approach does not seem well-suited when it is assumed that such offsets exist.