Error: a number, parameter, or probability distribution

The article considers the issue of formats adopted for the accuracy characteristics of results (representation by difference, scattering parameter, or distribution) in solving measurement problems under the theory of errors and the concept of uncertainty. It is shown that for the error as a difference, the key issue is that the so-called true value is unknown. For measurement uncertainty, the transition to estimating the scattering parameter using a series of repeated measurements and rejection of the adjective “true” raises a number of other issues: lack of statistical inference logic, the inconsistency between the term “confidence level” and the term “confidence probability” in state hierarchy schemes, and the practical uselessness of measurement uncertainty characteristics in risk analysis. The continuous improvement of methods and measuring instruments in the theory of errors and the infinite amount of information for a complete description of the measurand in the concept of uncertainty essentially represent a common drawback of both approaches. Conceptually, the transition from error to uncertainty is an intermediate step to the representation of accuracy characteristics by probability distributions. The author provides a brief overview of how the point of view in international metrology on this issue has evolved. Accuracy assessment of results is presented as the structural and parametric identification of drift in the metrological characteristics of measuring instruments and standards, as well as metrological certification of procedures for solving measurement problems in the cross-observation scheme in terms of probability distributions. This solves the problems associated with the inadequacy of other formats to represent accuracy characteristics. The format of probability distribution is shown to be the best characterization of accuracy for the theory of errors and the concept of uncertainty.