Tests to assess whether a given data set of measurement results is based on a multiplicative measurement model

Many of the statistical methods used at the IAEA, such as methods for determining sampling plans or estimating the random and systematic error variances of the operator and the inspector, assume that the reported measurement results are realizations of a multiplicative measurement model. A multiplicative measurement model relates the true value of the measurand (e.g. the mass of an item, the enrichment or concentration of material) multiplicatively to the random and systematic errors of the measurement. In practice, the assumption that the observed measurement results are based on a multiplicative measurement model is rarely checked but is implicitly assumed as a fact. However, to justify the statistical methods used at the IAEA, a prior assessment as to whether a multiplicative measurement model can be assumed for a given set of measurement results is mandatory. According to the abstract submitted January 2024, we wanted to present statistical tests tailored to the specific measurement situation addressed in this paper. Due to obstacles in estimating the parameters of the statistical model, we cannot present any of the promised statistical tests. Instead, we describe the approaches we chose and why they did not work. This description is intended to demonstrate future researchers in this field which approaches they are better off not pursuing.