Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error

Magnetic testing of steels ' mechanical properties is based on their correlation with steels ' magnetic parameters. The purpose of this work was to establish dependence of the attainable correlation coefficient R max between measurement results and the parameter values a on the reduced error of its measurement. The article proposes a model of the correlation field between the parameter true values and the results of its measurement with a given reduced error δ . The merits and legitimacy of using the model for estimation of the achievable correlation coefficient R max are substantiated. Analysis of influence of δ parameter measurement in different ranges d of its change on R max is carried out. Results are compared with the previous analysis for the relative measurement error. It has been established in this work that the coefficient R max calculated for the reduced measurement error is always smaller than R max one calculated for the relative measurement error. However in the practically important range of variation of d with δ ≤ 0.05 the difference between the R max values calculated for the reduced and relative measurement errors is not large. This allows us to use the developed formula for the dependence R max = R max (δ, d ) at R max ≥ 0.8 for both relative and reduced measurement errors δ . The obtained result allows us using the reduced measurement error of a metrologically certified measuring instrument to obtain the maximum attainable correlation coefficient between the true values and the results of measuring a parameter in a given range of its change without measurements. As an example, we define the conditions for the non-destructive testing of steels under which one can use measuring of magnetic parameters with the installation certified based on the reduced measurement error.