A Bayesian framework to update scaling factors for radioactive waste characterization

Nuclear power plants and research facilities commonly employ the so-called scaling factor (SF) method to quantify the activity of difficult-to-measure (DTM) radionuclides within their radioactive waste packages. The method relies on the establishment of a relationship between an easy-to-measure (ETM) radionuclide, called key nuclide (KN), and difficult-to-measure radionuclides, after the collection of a representative sample from the waste population. The distribution of the scaling factors, as well as the parameters defining the distribution, can change over time. Therefore, the accuracy of the calculated activity of the DTM radionuclides depends on the capacity of the scaling factor method to follow the time evolution of the waste population. In practice, waste producers collect periodically new samples from the waste population and check the variation and the validity of the scaling factors. In this article, we present a simple Bayesian framework to update scaling factors when a new data set becomes available. The method is tested and validated for radioactive waste produced at CERN (European Organization for Nuclear Research) and can be easily implemented for waste of different origin.