Hanford’s Decision Level for Alpha Spectrometry Bioassay Analyses Based on the Sample Specific Total Propagated Uncertainty

J.A. MacLellan, Radiation and Health Technology, Pacific Northwest National Laboratory, Richland Washington 99352.

The bioassay program for the entire Hanford workforce is managed by the Pacific Northwest National Laboratory. Until April 2000, the decision levels by which samples containing elevated quantities of radioactive material were identified were all specified in the contract with the analytical laboratory as absolute activity values. The contract specified an upper bound for the minimum detectable activity (MDA) for each analysis (the contract limit), and established the decision level at one-half the contract limit (CL). For most alpha spectrometry analyses the CL was 0.02 dpm per sample. The decision level was applied to the activity result, rather than the count data. The detection criterion was therefore insensitive to sample specific variables such as chemical yield and detector efficiency.

In order to select a better procedure, an investigation of the ANSI N13.30 and other proposed decision level equations was initiated. The investigation concluded that the ANSI N13.30 equation significantly underestimates the number of false positive results. The overestimation peaks at about one background count during the counting period, but remaines significant up to an expected 100 counts. The ANSI N13.30 equation answers the question “For a given background count rate, how large a net count will be observed less than “alpha” percent of the time, if there is no activity in the sample?” An equation proposed by Altshuler and Pasternack in 1963 was found to be far superior. That equation answers the question “How much activity can be in a sample, and the confidence interval for the net count still include zero?" The decision level obtained from the Altshuler and Pasternack equation remains unbiased down to an expected three counts during the counting period.

The concept of the Altshuler and Pasternack equation was adopted for the Hanford bioassay program, but an additional simplification was incorporated. The actual form of the equation used in our previous investigation calculates the decision level based only on the number of observed background counts. However, the original form of the equation used in the derivation equates the decision level with a multiple of the variance estimate of a net count value (-₁). That is, the decision level is derived from the following equation_:

by solving for -₁, where n_g is the gross count, and n_b is the background count. The decision level (in net counts) is therefore equal to

Because the Hanford bioassay contract requires an estimate of the total propagated uncertainty (TPU) for each result reported, it is simple to implement a sample specific decision level based on the TPU. Rather than using the second equation, Hanford alpha spectrometry decision levels are set from the first equation, substituting the TPU for the radical. A k_I value of 2 was chosen in order to maintain the average decision level near historic levels. The decision level then takes the following simple form:

Decision Level = 2(TPU)

This decision level has been used in its empirical form for many years. With this equation, about two percent of the results are expected to be false positives assuming a normal distribution of the net count.

(Prepared in connection with work done under Contract Number DE-AC06-76RLO 1830 with the United States Department of Energy. )