The evaluation of key comparison data: determining the largest consistent subset

Abstract

Suppose a single stable travelling standard is circulated around the national metrology institutes (NMIs) participating in a key comparison. Consider the set of data consisting of a measurement result, comprising a measured value and the associated standard uncertainty, provided independently by each such NMI. Each measured value is the corresponding NMI's best estimate of a single stipulated property of the standard. The weighted mean (WM) of the measured values can be formed, the weights being proportional to the reciprocals of the squared standard uncertainties. If this WM is consistent with the measured values according to a statistical test, it can be accepted as a key comparison reference value for the comparison. Otherwise, the WM of a largest consistent subset (LCS) can be determined. The LCS contains as many as possible of those results of participating NMIs that are consistent with the WM of that subset. An efficient approach for determining the LCS having smallest chi-squared value is described, and applied to length, temperature and ionizing radiation comparisons.

Key comparisons: the chance for discrepant results and some consequences

“…This paper only refers to indirect methods. Actually, in the vast majority of cases and for sufficiently high accuracy a direct method is only an ideal approximation, since, due to the corrections, 12 the number of influence quantities is higher than that strictly required for the direct method.…”

A support of metrological traceability of inductance measurements in Ukraine

“…In [12], a general approach for evaluation of KC results is presented, in [13] -clarification of a general approach to the determination of the largest successive subset, in [14] -an example of the model of selection in the average of inconsistent data. However, in many practical cases of evaluation of comparison results, it is quite difficult and sometimes impossible to apply the specified approaches in practice.…”

Verification of Statistical Calculations in Interlaboratory Comparisons by Simulating Input Datasets

“…Approaches in organization and statistical evaluation of the results can be very different and depend on the aim of an interlaboratory comparison, number of participants, their quality, form of results, etc. [10,11]. In order to enable validation of statistical calculations in all possible types of interlaboratory comparisons, we have developed a special software application [12,13] that allows the user to choose between different types of comparisons in calibration and testing.…”

“…The user can select boundary conditions for generating data sets and statistical quantities to be calculated. The software is offering different selection possibilities by following general rules for comparisons in calibration [2,3,10,11] and in testing [4].…”