A Test of Linearity Using Covering Arrays for Evaluating Uncertainty in Measurement

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. Nowadays 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 for 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. If the fitting algorithm is sufficiently robust a linear model is derived from the fitting algorithm which is then used in a second step to evaluate the uncertainty of the fitting parameters. This paper discusses the sensitivity analysis in detail with the emphasis on possibilities to check for robustness and linearity. An efficient method based on covering arrays is presented to test for hidden couplings between the input parameters inside the evaluation model.