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

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.