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.

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Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system.

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.

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