Error is a number, parameter or probability distribution
Authors: Levin S. F. 
Published: September 2024

The problem of the format (the form of representation by difference, scattering parameter, distribution) of the characteristics of the accuracy of the results in solving measurement problems in terms of the theory of errors and the concept of uncertainty is considered. It is shown that for the error as a difference, the key question is the uncertainty of the so-called true value. For measurement uncertainty, when switching to estimating the scattering parameter based on a set of repeated measurements and getting rid of the adjective true, a number of key issues of a different plan arise – the lack of logic of statistical inference, the inconsistency of the term “confidence level” with the term “confidence probability” in state verification schemes and the practical uselessness of measurement uncertainty characteristics in risk analysis tasks. However, the endless improvement of measurement methods and tools in the theory of errors and an unlimited amount of information for a complete description of the measured value in the concept of uncertainty is a common defect of both approaches, only in other words. Conceptually, the transition from error to uncertainty is an intermediate stage to the representation of accuracy characteristics by probability distributions. A brief overview of the transformation of the point of view of international metrology on this issue is given. The evaluation of the accuracy of the results is presented as a structural-parametric identification of the drift of metrological characteristics of measuring instruments and standards, as well as metrological certification of methods for solving measurement problems in the cross-observation scheme in terms of probability distributions. This allows you to get rid of the problems of incompleteness of other formats for representing accuracy characteristics. The most complete characterization of accuracy for the theory of errors and the concept of uncertainty is the format of the probability distribution. However, the endless improvement of measurement methods and tools in the theory of errors and an unlimited amount of information for a complete description of the measured value in the concept of uncertainty is a common defect of both approaches, only in other words. Conceptually, the transition from error to uncertainty is an intermediate stage to the representation of accuracy characteristics by probability distributions. A brief overview of the transformation of the point of view of international metrology on this issue is given. The evaluation of the accuracy of the results is presented as a structural-parametric identification of the drift of metrological characteristics of measuring instruments and standards, as well as metrological certification of methods for solving measurement problems in the cross-observation scheme in terms of probability distributions. This allows you to get rid of the problems of incompleteness of other formats for representing accuracy characteristics. The most complete characteristic of accuracy for the theory of errors and the concept of uncertainty is the format of the probability distribution.