Design of experiment for evaluation of uncertainty from sampling in the framework of the fitness for purpose concept: a case study

The design of an experiment for the evaluation of sampling uncertainty in the framework of the fitness for purpose concept is described in terms of probabilities (risks of the user) of type 1 and type 2 errors in decisions concerning the significance of effects influencing the sampling uncertainty and the measurement results. As a case study, an experiment based on the duplicate method for quantification of the sampling uncertainty and inhomogeneity (heterogeneity) of a melt of tin-free bronze produced in a 10-ton reflective oven is analyzed. The melt is defined as the sampling target. It is shown that the number of such targets (melts), the number of samples under analysis and the number of replicate analyses can be minimized, i.e., the size and cost of the experiment can be reduced, if the user knows which risks are acceptable. When inhomogeneity of the sampling target has a systematic character, like the decrease of the mass fraction of aluminum from the beginning to the end of the melt pouring in the case study, the inhomogeneity effect can be separated from the sampling uncertainty and evaluated according to the user’s needs.