Evaluation of eight decision rules for low-level radioactivity counting

In low-level radioactivity measurements, it is often important to decide whether a measurement differs from background. A traditional formula for decision level (DL) is given in numerous sources, including the recent ANSI/HPS N13.30-1996, Performance Criteria for Radiobioassay and the Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM). This formula, which we dub the N13.30 rule, does not adequately account for the discrete nature of the Poisson distribution for paired blank (equal count times for background and sample) measurements, especially at low numbers of counts. We calculate the actual false positive rates that occur using the N13.30 DL formula as a function of a priori false positive rate a and background Poisson mean mu = rhot, where rho is the underlying Poisson rate and t is the counting time. False positive rates exceed a by significant amounts for alpha < or = 0.2 and mu < 100 counts, peaking at 25% at mu approximately equal to 0.71, nearly independent of alpha. Monte Carlo simulations verified calculations. Currie's derivation of the N13.30 DL was based on knowing a good estimate of the mean and standard deviation of background, a case that does not hold for paired blanks and low background rates. We propose one new decision rule (simply add 1 to the number of background counts), and we present six additional decision rules from various sources. We evaluate the actual false positive rate for all eight decision rules as a function of a priori false positive rate and background mean. All of the seven alternative rules perform better than the N13.30 rule. Each has advantages and drawbacks. Given these results, we believe that many regulations, national standards, guidance documents, and texts should be corrected or modified to use a better decision rule.