Evaluations of key comparisons based on the probability distributions for the participating institutes' measurement quantities.

摘要

If only the values and the associated uncertainties of the participating institutes' measurements in a key comparison are provided, a Gaussian probability density function (PDF) is assigned for each measured quantity. In reality however, the PDFs may not be Gaussian. The evaluation of the key reference value (KCRV) and the degrees of equivalence (DOE) depend on the PDFs. Given a model that relates the participating institutes' measurements to a KCRV, it is proposed that the PDF for KCRV and the DOEs are determined by propagating the PDFs for the quantities measured by the participating institutes. The propagation of PDFs is shown to be more generally applicable than the propagation of uncertainties. It can be used with any model and treats elegantly correlation and problems associated with a small number of repeated measurement and, last but not least, it provides insight to the underlying measurement problems. This paper provides an introduction to Monte Carlo techniques that are ideal tools for propagating PDFs. Using simulated data, several models for the evaluation of key comparisons are discussed and the influence of correlation is examined. One of these models is based on the median. Only Monte Carlo techniques and to some extent bootstrapping techniques are capable to compute the uncertainty associated with the value of the median.