Narrow Results

Modelling of a measurement is an indispensable prerequisite of modern uncertainty evaluation. Both, the ISO-GUM [1] and the supplement of the GUM [2] require to express the knowledge about the measurement process by a so-called model equation which represents the mathematical relationship between the relevant parameters, the influence quantities, the indication and the measurand(s). Nevertheless both documents are confined to lumped-parameter systems in the steady state. Since dynamic measuring systems gain more and more importance, modern uncertainty determination must develop appropriate modelling approaches for dealing with dynamic measurements. This paper exemplary describes a possible modelling approach for dynamic measurements that utilizes discretised state-space forms.

The Guide to the Expression of Uncertainty in Measurement (GUM) is self-consistent when Bayesian statistics is used for the Type A evaluations. We present the case that there are limitations on the kind of Bayesian statistics that can be used for the Type A evaluations of input quantities of the measurement function. The GUM recommends that the (central) measured value should be an unbiased estimate of the corresponding (true) quantity value. Also, the GUM uses the expected value of state-of-knowledge probability distributions as the (central) measured value for both the Type A and the Type B evaluations of input quantities. It turns out that the expected value of a Bayesian posterior distribution used as a Type A (central) measured value for an input quantity can be unbiased only when a non-informative prior distribution is used for that input quantity. Metrologically, this means that only the current observations without any additional information should be used to determine a Type A (central) measured value for an input quantity.