A Test of Linearity Using Covering Arrays for Evaluating Uncertainty in Measurement
Ruediger Kessel, Raghu N. Kacker
Since the Guide to the Expression of Uncertainty in Measurement (GUM) was published in 1993 it has changed the evaluation of physical and chemical measurements. In our days almost all high level measurements include a detailed evaluation of uncertainty. This allows the scientific community to do the next step and evaluate uncertainty for derived evaluations like parameter fittings. The evaluation of the uncertainty of complicated parameters like the results from non-linear fitting procedures can be carried out in two steps. The first step is a sensitivity analysis of the evaluation algorithm and a test of mutual independence of the parameters. In case the fitting algorithm is sufficiently robust a linear model is derived from the fitting algorithm which is than used to evaluate the uncertainty of the fitting parameter. The paper will discuss the procedure in detail with the emphasis on possibilities to check for robustness and linearity. An efficient method based on covering array will be presented to check for hidden couplings between the input parameter inside the evaluation model.
Advanced Mathematical and Computational Tools in Metrology AMCTM VIII