Components of Variance in Liquid Scintillation Counting

As part of the standardization of the ²³⁹Pu solution that was disseminated by NIST as Standard Reference Material (SRM) 4330C, a detailed study was performed to better understand and ascertain how to treat the underlying principal components of variance in liquid scintillation (LS) counting.

These components arise from the variability effects that occur when using different commercial LS counters, from differences in the use of counting sources with varied cocktail compositions, and from temporal dependencies. The experimental design consisted of looking at a matrix of results from three significantly different cocktail compositions with five replicate counting sources for each composition as measured with three different LS counters at varying times. The work was augmented by also re-examining data from standardizations of other radionuclides, including those for ⁶³Ni, ⁹⁰Sr, ²¹⁰Pb, ²³⁹Pu, ²⁴¹Pu, and ²⁴¹Am, which have been performed over the past few years by our laboratory. Simple graphical techniques as well as more classical, rigorous statistical methods (e.g., multi-factor ANOVA) are readily available to look for such effects. Failure to do so can result in unrealistic precision estimates, with an attendant serious underestimation of the inherent measurement uncertainties. The throwing of all measurement values into one calculation pot – without looking – and calculating a standard deviation of the mean is an abuse of the Central Limit Theorem. The existence of multiple variance components may be present and missed unless one uses well-designed experiments to look for them and then appropriately examines the data by analytical methods. Real standardization data, both homogeneous like that for ²³⁹Pu and heterogeneous like that for ²¹⁰Pb and ²⁴¹Pu, readily demonstrate these points. For example, in the standardization of ²¹⁰Pb, the minimum relative standard deviation of the mean (< 0.01%) obtained when ignoring the within- and between-counter (on subsequent measurement occasions) variance components results in a precision estimator that is a factor of 12 times less than a more realistic estimate. For ²⁴¹Pu, which exhibited substantial between-counter and between-composition variability effects, the all-in-one-pot standard deviation of the mean underestimates the realistic measurement precision by a factor of 8. Other standardization results have effects that are similarly pronounced. These were important findings for our understanding of LS counting, which is one of the most important measurement work horses used by the Radioactivity Group