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

摘要

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.