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 delta. The merits and legitimacy of using the model for estimation of the achievable correlation coefficient R-max are substantiated. Analysis of influence of delta 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 delta <= 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 (delta, d) at R-max >= 0.8 for both relative and reduced measurement errors delta. 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.