Introductory Statistical Methods for Radiological Characterization of Radioactive Waste

This paper provides a comprehensive overview of statistical methods employed in sample-based radiological characterization of radioactive waste (RAW), with a particular focus on the use of nuclide vectors (NVs) and scaling factors (SFs) as applied in commercial RAW characterization projects. These methods are crucial for estimating the activity of difficult-to-measure (DTM) radionuclides by establishing correlations with easy-tomeasure (ETM) key nuclides (KNs), thereby minimizing the need for time-consuming and costly radiochemical analyses. A scaling factor (SF) is defined as the ratio of the activity (or specific activity) of a DTM to that of a corresponding KN in a given sample. The applicable standard deviation (SF) is typically determined as the geometric mean of the standard deviations (SDs) calculated from all samples, providing a robust and statistically representative value. The nuclide vector (NV) represents the relative distribution of individual radionuclides within the total activity of a sample or waste stream. NVs are recommended to be derived using the one-sigma concept, which assumes that approximately 68% of all possible values fall within a defined acceptance range, improving statistical confidence. For NVs and SFs to be valid, the underlying datasets must meet several criteria: they must be representative, span a wide range of activity levels, and be statistically homogeneous, meaning they follow a standard or log-normal distribution. Additionally, datasets must be free from significant outliers, typically identified using the Grubbs test, and show adequate correlation between radionuclides, assessed via Pearson or Spearman correlation coefficients. The methodology is demonstrated using data from 10 samples containing Mn-54, Co-60, Nb-94, Fe-55, Ni-63, and Sr-90. Results confirm that the calculated NVs and SFs are statistically valid and representative, supporting their practical application in modern RAW characterization.