Analysis of key comparison data and laboratory biases

Abstract

The analysis of key comparison data is at the focus of metrology-related research and many papers have been published on this issue in recent years. Typically, the approaches make use of quoted combined uncertainties. We propose an approach which is based on more detailed uncertainty information. We assume that each of the participating laboratories has knowledge about the precision of its measurements and, in addition, provides a probability density function (PDF) which encodes its assessment on the size of its bias. Only the case of a single stable travelling standard is considered.The analysis starts with a consistency test of the data and the PDFs provided by the participating laboratories. If this test is passed, a probabilistic approach based on a bias model is applied in order to merge the information of all participants. PDFs for the value of the travelling standard and, in particular, for the biases of the participating laboratories are derived. Explicit results are given for Gaussian PDFs. It is shown that the proposed use of detailed uncertainty information results in improved estimates of the biases. In particular for those laboratories expecting to have a large bias, the uncertainty about their biases can thereby be reduced significantly.

Weighted means statistics in interlaboratory studies

“…Before that we note that model (6) may not help to understand possible systematic influences on the measurement results of one or several labs [18].…”

Assessing interlaboratory comparison data adjustment procedures

“…The 95th percentile for x 2 10 isc 2 ¼ 18:3 while its mean is 10 which in fact corresponds to the 56th percentile, P (x 2 < 10) = 0.56. (The 50th percentile, in other words the median, of a x 2 n distribution is approximately n(1 À 2/(9n)) 3 and is somewhat less than its mean, due to the skewness of the distribution.) Thus, if R 2 0 ¼ 18:5, above the threshold, an adjustment procedure will be applied to achieve a value of R 2 (v) = 10, while if R 2 0 ¼ 18:1, less than the threshold, no adjustment procedure is applied.…”

“…If the data is judged to be inconsistent, the WLS estimate a might not be a reliable estimate of a in the sense that the variance matrix V a may underestimate the uncertainty associated with this estimate. In the presence of inconsistency, a procedure can be applied to adjust the uncertainties to achieve consistency, see, e.g., [2][3][4][5][6][7][8][9][10]. The underlying assumption behind these approaches is that some or all of the laboratories have underestimated or neglected some uncertainty contributions, sometimes referred to as 'dark uncertainty' [11], and the adjusted uncertainties implicitly provide an estimate of this dark uncertainty derived from the complete set of laboratory results.…”

Reviving the inter-laboratory comparison measurement results

“…Conceptually, the corrective action belongs to the jurisdiction of the participant. The work carried out (Chunovkina, 2008) for improving the estimation of bias of intercomparison assume that the probability density function (PDF) that encodes the size of its bias is available and results are consistent. Otherwise, the uncertainty about their biases cannot be reduced.…”