Józef Wiora

A weighted method for reducing measurement uncertainty below that which results from maximum permissible error

According to recent findings, it is possible to computationally determine a measurement result (value and uncertainty), using a special measurement method, in which this uncertainty is less than that assessed directly from experiments using Type B evaluation. The method works well only if the quantity is additive and its uncertainty is constant, i.e. independent of the measurement value. In the paper, a generalisation is made that also allows for the application of similar reasoning to quantities with variable uncertainties. The generalisation is obtained thanks to the replacement of the least squares optimisation, used in the derivation of the first method, with the weighted least squares. Examples with models of quantities that have variable uncertainties are described to show circumstances where improvements are significant. It can be said that the method described always improves uncertainties of additive quantities, but the improvement is not always significant. Suggestions to obtain the best improvement are given according to the analysis performed. A real laboratory experiment of a resistance measurement, with its uncertainty dominated by current measurement, was conducted to show how the method works.

Calibration of potentiometric sensor arrays with a reduced number of standards

In this paper a novel calibration procedure for the parameter determination of ion-selective electrodes used in an array is described. Commonly used procedures require a large number of standards to determine the parameters based on the Nicolsky-Eisenman model. The elaborated procedure reduces the number of standards to a minimum by using a standard containing a mixture of ions instead of a couple of pure standards. This paper presents a complete calibration procedure, which consists of designing the composition of the standards, parameter determination and verification of the calibration results. Comparison of the results obtained by the procedure presented with results obtained by the Two-Point Calibration and Separate Solution methods proves that the accuracies of both procedures are comparable. The outlined procedure can be applied in multicomponent analysers.

Problems and risks occurred during uncertainty evaluation of a quantity calculated from correlated parameters: a case study of pH measurement

Parameters of a model describing a measurement process obtained during a calibration experiment allow one to calculate a measurement result, but a simple estimation of measurement uncertainties of the parameters is not sufficient to assess the uncertainty of the result. In this paper, an example of a pH measurement conducted using an ion-selective electrode is presented, in which the uncertainty is evaluated taking into consideration the existing correlation between the parameters of the electrode. The calculations apply either covariances or correlation coefficients that have to be computed additionally. The example presented in this paper illustrates that there are some problems with rounding of variables which, because of the existing very strong correlations, significantly changes the sought uncertainty. This approach is compared with other approaches, that is, usage of uncorrelated variables and Monte Carlo simulations that are described in an earlier work. It is concluded that the approach of uncertainty evaluation, in which covariances or correlation coefficients are explicitly calculated, is work-consuming and may cause significant discrepancies between correct and obtained assessments if some roundings or approximations are done, or if the correlation coefficient is obtained experimentally based on data including random errors.

Uncertainty Evaluation of pH Measured Using Potentiometric Method

Determination of pH using a typical glass electrode requires prior calibration in order to determine the electrode parameters. Knowledge about uncertainties of the parameters is insufficient to calculate the uncertainty of measured pH because of existing correlation. In the paper, an example illustrating the problem is presented. Two ways of proper uncertainty assessment are suggested: (1) analytical with removing the correlated variables and (2) numerical using Monte Carlo simulations. The second one seems to be much less time-consuming and allows easier investigations of the uncertainty properties.

A system allowing for the automatic determination of the characteristic shapes of ion-selective electrodes

The plot of ion-selective electrodes potential vs. ion concentration in a solution is non-linear and very complex. In the paper, a set-up is described which allows to determine the plot using multiple dilution method in an automatic way. The set-up is not expensive and the presence of experimenter in the laboratory is not necessary during the test of the electrode. Additionally, the system allows for simultaneous investigation of several electrodes.

Measurement Uncertainty Calculations for pH Value Obtained by an Ion-Selective Electrode

An assessment of measurement uncertainty is a task, which has to be the final step of every chemical assay. Apart from a commonly applied typical assessment method, Monte Carlo (MC) simulations may be used. The simulations are frequently performed by a computer program, which has to be written, and therefore some programming skills are required. It is also possible to use a commonly known spreadsheet and perform such simulations without writing any code. Commercial programs dedicated for the purpose are also available. In order to show the advantages and disadvantages of the ways of uncertainty evaluation, i.e., the typical method, the MC method implemented in a program and in a spreadsheet, and commercial programs, a case of pH measurement after two-point calibration is considered in this article. The ways differ in the required mathematical transformations, degrees of software usage, the time spent for the uncertainty calculations, and cost of software. Since analysts may have different mathematical and coding skills and practice, it is impossible to point out the best way of uncertainty assessment—all of them are just as good and give comparable assessments.

Application of Artificial Neural Networks for Modelling of Nicolsky-Eisenman Equation and Determination of Ion Activities in Mixtures

The paper deals with the problem of ion activity determination for a mixture by means of ion-selective electrodes. Mathematical model of the analysed phenomenon is described by the Nicolsky-Eisenman equation, which relates activities of ions and ion-selective electrode potentials. The equation is strongly nonlinear and, especially in the case of multi-compound assays, the calculation of ion activities becomes a complex task. Application of multilayer perceptron artificial neural networks, which are known as universal approximators, can help to solve this problem. A new proposition of such network has been presented in the paper. The main difference in comparison with the previously proposed networks consists in the input set, which includes not only electrode potentials but also electrode parameters. The good network performance obtained during training has been confirmed by additional tests using measurement results and finally compared with the original as well as the simplified analytical model.