Uncertainty Analysis of MSL’s CCT-K7.2021 Key Comparison Measurements Taking Account of Correlations

The National Research Council of Canada (NRC) recently piloted the second international key comparison of triple point of water (TPW) cells, CCT-K7.2021, where the measurand was the difference between the temperature realised by a transfer cell selected by each participant and the temperature attributed to that participant’s national reference. By comparing the differences between each transfer cell, NRC could calculate the differences between each participant’s national reference. While there was good agreement among all the participants, there was a large variation among the uncertainties in the submitted measurand estimates. This was possibly due to the complexity of the uncertainty analysis, which typically has many correlated components that partially cancel when the correlations are treated carefully. The Measurement Standards Laboratory of New Zealand (MSL) carried out its analysis using the algorithmic method of uncertain numbers. This method rigorously represents a measurement model for the calculation of uncertainty so that the effects of common influence factors—which can lead to correlations—are properly accounted for. MSL carried out this analysis using a Python software package called the GUM Tree Calculator (GTC). As a consequence, MSL submitted an uncertainty value less than half of the uncertainty values submitted by almost all of the other participants. This paper describes the measurement model implemented by MSL and demonstrates the use of GTC in carrying out the uncertainty analysis. The paper also shows how applying GTC to the previously published NRC analysis results in a reduction in the NRC uncertainty.