Components of a Variance Model for the Analysis of Repeated Measurements in Fixed-Point Comparisons

Experimental design is a statistical tool concerned with the planning of experiments to obtain the maximum amount of information from the available resources. This tool may be applied to metrology, especially for the analysis of a large number of repeated measurements (replicates) of short-term repeatability and the medium-term and long-term reproducibilities, enabling the inclusion of these “time-dependent sources of variability” in the uncertainty budget. The realization of the International Temperature Scale of 1990 (ITS-90) scale requires that laboratories usually have more than one cell for each fixed point, for comparison on a regular basis. The calculation of the uncertainty of such comparisons is considered here, taking into account these time-dependent sources of variability. These components of the uncertainty evaluated by a Type A method are obtained by the statistical analysis of the experimental results using the components of a variance model for designs consisting of nested or hierarchical sequences of measurements, as foreseen by the mainstream GUM. An application example of a balanced nested structure in the comparison of two fixed-point cells is presented.