Developing and using measurement models to assess accuracy: using the example of measurements of the activity of ions

What is it about?

Evaluating the measurement accuracy of sensors is one of the most important tasks in the development of support systems for Industry 4.0. The study of accuracy is proposed to be carried out using measurement models by expanding them into a Taylor series. From the components of the Taylor series, equations are obtained that describe the sensitivity, additive and multiplicative errors of the measuring instrument. A mathematical model is also proposed that allows you to recalculate the multiplicative and additive errors of the measuring instrument into the uncertainty. The proposed metrological models are tested on the example of the expansion of the transformation equation, which describes the operation of the means for measuring the activity of ions. In absolute units of measurement of ion activity, the multiplicative and additive errors are 0.047pX each in the measurement range from 0.2 to 7.5pX. Using proposed mathematical model for converting these errors into uncertainty, we obtained the standard type B uncertainty, which is 0.064pX.

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Why is it important?

The goal of this paper is to develop a metrological model to refine the calculation of analytical expressions for the additive errors and multiplicative errors present for measuring the activity of ions of the constituent elements of humus in the soil in terms of an analysis of the models associated Taylor series in order to estimate the models’ a priori type B uncertainties. The basic performances of instruments include additive and multiplicative errors, measurement range, and errors in the instruments. These metrological performances are sufficient to establish standards for the accuracy of the measurement instruments.