The concept of uncertainty and error theory: philosophy and mathematics

Abstract

The article is devoted to the consideration of the recent problem of the relationship of mathematical results and terminology in metrology. Various approaches to solving the problem of identifying the measurand are analyzed: the Monte Carlo method, the composition of the computation errors and the errors obtained at calibration of the instrument; composition of inadequacy errors.The history of development of the term “measurement” is considered. The difference in types of measurements and names of computational operations is pointed out. The consideration of the probability density of the measurand in the object model for the correct assessment of measurement accuracy is substantiated.The terms “confidence interval” and “level of confidence” are analyzed, as well as the differences between their use in mathematical statistics and the concept of uncertainty.The term “definitional uncertainty” as a measure of the threshold nonconformance between the model and the object of measurement is analyzed. It is shown that the definitional uncertainty is an unknown and unknowable quantity.The features of various concepts of probability are considered: the combinatorial-axiomatic concept of Moivard–Laplace; Poisson–Mises frequency concept; Bernoulli–Bayes subjective concept; Gauss–Fisher–Kolmogorov interpolation concept.The analysis of the thermometer calibration problem solution is carried out using different models: models in the form of a continuous correction function; the regression model and the model obtained by structural-parametric identification by the criterion of the minimum average modulus of inadequacy error by the method of K. Jacobi. The differences in the results obtained when applying different models are shown. It is concluded that the calibration results using “Guides to the Expression of Uncertainty in Measurement” are inconsistent with the main objective of the Law “On ensuring the uniformity of measurements”.The task in set on the necessity of restructuring the documents of the state system for ensuring the uniformity of measurements in order to achieve their harmonization.