Impact of the number of material measurement categories on measurement error

There is nearly always some mismatch between the physical properties of items containing nuclear material and standards used to calibrate the assay method. Physical properties include the density and heterogeneity of the item's nonnuclear material and the type of interfering species, such as hydrogen in the case of neutron counting. Some assay techniques are less sensitive to variation in physical properties than others and can be used to generate working standards. Provided that a reference assay method 1 (often calorimetry) is available that is well characterized (having negligible or known dependence on varying physical properties), we can assess the total measurement error of another method 2. In this paper we consider the impact of the number of measurement categories on the measurement error standard deviation of method 2. We assume that working standards (traceable to primary reference standards) are provided by the method 1 assay of actual facility items. Given the same number of working standards, we evaluate the tradeoff between using more working standards for each of a fewer number of categories versus using fewer standards in each of more categories. This leads to a method to determine a good allocation of working standards.