The problem of inadequacy: cosmology and metrology. Part 2. Definite uncertainty

The problem of expressing measurement uncertainty associated with the incompleteness of the description of mathematical models of measurement objects is considered. Various viewpoints on the main document “Guide for Expressing Measurement Uncertainty” and its translation into Russian have been discussed. It is shown that the condition of applicability of this document is necessarily strict: the insignificant uncertainty caused by the inadequacy of the model must be ensured not only with respect to the required accuracy of the result, but also with respect to other components of the uncertainty budget. In principle, the document under consideration indicates the correct way to solve this problem: the use of empirical measurement models, long-term data, comparison standards, and control charts that can show whether the measurement is under statistical control. However, this logic is not fully developed. This paper describes a cross-observation scheme for inadequacy errors in equal-precision and unequal-precision measurements. It analyzes an example of solving the measurement problem of thermometer calibration from Appendix H.3 of the “Guide for the Expression of Measurement Uncertainty” for the correction function. The recommended solution is to use a cross-examination scheme for sample variance or standard deviation.