Expression of calibration and measurement capabilities of accredited calibration laboratories in a measurement range

The expression of calibration and measurement capabilities (CMCs) of accredited calibration laboratories in a range of values is analysed, and the insurance of appropriate linear interpolation to find the measurement uncertainty at average values is considered. To minimize the expanded measurement uncertainty, it is proposed to calculate the coverage factor using the kurtosis method so that it would correspond to the composition of the distribution laws of the input quantities. To approximate the laboratory calibration and measurement capabilities when expressing them as an explicit function of the measurand, it is proposed to apply the least squares method. For non-polynomial dependencies, the capabilities shall be first transformed by replacing the variables into linear ones, which shall be followed by using the least squares method. To facilitate the approximation of CMCs, the use of the “trend line” function of MS Excel is proposed. Four additional nonlinear functions are considered, which are approximated by hyperbolic and homographic functions of Types 1 and 2, as well as by quadrature addition, which can also be transformed into a linear function, and the estimates of their parameters can be obtained by using the least squares method. An example of performing the approximation by various functions of calibration and measuring capabilities of a laboratory when calibrating a digital caliper is considered.