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 Rmax between measurement results and the parameter values a on the reduced error...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Belarusian National Technical University
2019-03-01
|
| Series: | Приборы и методы измерений |
| Subjects: | |
| Online Access: | https://pimi.bntu.by/jour/article/view/428 |
| _version_ | 1826557415058833408 |
|---|---|
| author | S. G. Sandomirski |
| author_facet | S. G. Sandomirski |
| author_sort | S. G. Sandomirski |
| collection | DOAJ |
| description | 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 Rmax 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 Rmax are substantiated. Analysis of influence of δ parameter measurement in different ranges d of its change on Rmax 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 Rmax calculated for the reduced measurement error is always smaller than Rmax 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 Rmax values calculated for the reduced and relative measurement errors is not large. This allows us to use the developed formula for the dependence Rmax = Rmax (δ, d) at Rmax ≥ 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. |
| first_indexed | 2024-04-10T01:37:15Z |
| format | Article |
| id | doaj.art-afa2a3cfa564410bab1f501029376a62 |
| institution | Directory Open Access Journal |
| issn | 2220-9506 2414-0473 |
| language | English |
| last_indexed | 2025-03-14T08:28:14Z |
| publishDate | 2019-03-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Приборы и методы измерений |
| spelling | doaj.art-afa2a3cfa564410bab1f501029376a622025-03-02T13:03:50ZengBelarusian National Technical UniversityПриборы и методы измерений2220-95062414-04732019-03-01101909810.21122/2220-9506-2019-10-1-90-98343Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement ErrorS. G. Sandomirski0Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus,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 Rmax 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 Rmax are substantiated. Analysis of influence of δ parameter measurement in different ranges d of its change on Rmax 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 Rmax calculated for the reduced measurement error is always smaller than Rmax 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 Rmax values calculated for the reduced and relative measurement errors is not large. This allows us to use the developed formula for the dependence Rmax = Rmax (δ, d) at Rmax ≥ 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.https://pimi.bntu.by/jour/article/view/428magnetics measurementserror of measurementlinear regression equationcorrelation coefficient |
| spellingShingle | S. G. Sandomirski Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error Приборы и методы измерений magnetics measurements error of measurement linear regression equation correlation coefficient |
| title | Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error |
| title_full | Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error |
| title_fullStr | Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error |
| title_full_unstemmed | Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error |
| title_short | Dependence of the Correlation Coefficient Between the Results of a Parameter Measurement and Its True Values on the Reduced Measurement Error |
| title_sort | dependence of the correlation coefficient between the results of a parameter measurement and its true values on the reduced measurement error |
| topic | magnetics measurements error of measurement linear regression equation correlation coefficient |
| url | https://pimi.bntu.by/jour/article/view/428 |
| work_keys_str_mv | AT sgsandomirski dependenceofthecorrelationcoefficientbetweentheresultsofaparametermeasurementanditstruevaluesonthereducedmeasurementerror |