On the analysis of measurement comparisons

The method of constrained least squares is applied to the determination of laboratory bias and degrees of equivalence in the analysis of measurement comparisons. The analysis assumes a measurement model with unknown values for all travelling artefacts and laboratory biases. Least-squares fitting applied to this model yields an infinite set of solutions, all with the same inter-laboratory and inter-artefact differences. The application of a constraint, which can be interpreted as the definition of the key comparison reference value, then yields a single solution. Different types of constraint may be applied for known-value comparisons, for key comparisons without known values, and when linking regional metrology organization or supplementary comparisons to key comparisons. Once the laboratory biases are determined, the degrees of equivalence can be determined using the generic equations provided. The constrained-least-squares approach provides a single mathematical framework for the analysis of a wide range of comparisons including those with multiple artefacts of varying attributes, circulated amongst multiple overlapping comparison loops, laboratories that provide an arbitrary number of measurements of one or more of the artefacts, and spectral dependence of laboratory bias.