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Measuring task calibration measurement means

S. Levin
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Description: The measuring task of calibrating measuring instruments is considered, the solution of which involves identifying a conversion function or correction function of a calibrated measuring instrument, finding its calibration characteristic or calibration diagram, which requires a probabilistic estimate of possible values of the output variable in the equation of the indirect measurement method according to probabilistic estimates input variables. Using the example of solving the measurement problem of thermometer calibration for measurement data from the international guide “Guide to the Expression of Uncertainty in Measurement” (GUM), we compared the results of solving a problem based on three approaches to the accuracy estimation: classical linear regression analysis, momentary and compositional approaches. Classic linear regression analysis provides an estimate of the accuracy of the result in the form of a confidence zone of a calibration curve. The GUM sub-approach qualifies as a momentbased method based on the construction of interval accuracy estimates based on the second-order moment estimates of the input variables of the indirect measurement method equation. At the same time, the compositional approach uses the method of functional transformations to obtain the distribution of the output variable as a composition of the distributions of input variables followed by the construction of a tolerant interval or tolerance zone as the most complete estimate of the accuracy of the output variable of the indirect measurement method. It is shown that for the data of the GUM thermometer calibration problem from the GUM, the ratio of the sizes of the coverage interval, the confidence and tolerance intervals is respectively 0.188:1:0.478 with the likelihood of grip and confidence probability equal to 0.95. The difference in accuracy estimates is caused by the difference in the formulation of the objective of the measurement task. If in the GUM moment approach, a proper estimate of measurement uncertainty is not the variance of the quantity sought, but its average arithmetic variance, then in the compositional approach the basic accuracy estimate is the stochastic tolerance interval.


Keywords: measuring instrument, conversion function, error function, correction function, calibration, calibration, confidence probability, tolerance interval

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Reference:
Levin, S.F. (2018), “Izmeritelnaia zadacha kalibrovki sredstva izmerenii” [Measuring task calibration measurement means], Information Processing Systems, Vol. 4(155), pp. 120-127. https://doi.org/10.30748/soi.2018.155.17.