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.