A proposed method to determine the decision level for radioactivity measurements

When measuring radioactivity, the problem rises of deciding whether or not a sample contains radioactivity in excess of background and above which value the result is meaningful. This decision process is why the notion of decision level was introduced. Whereas there is unanimity about its definition, this is not the case for its calculation, and many expressions have been proposed. This article contains a comparison of several decision level models by means of the calculation of actual false positive probability. First, three models are compared for the case of a well-known background, then a proposed model is developed and the four models are compared for the case of a poorly-known background. It appears from this study that, in order to be valid, the formula of the decision level must verify three conditions. First, the counting times have to appear symmetrically in the formula of the decision level; second, for long background counting times, the expression has to be equivalent to the one obtained with the corrected normal distribution corresponding to the Poisson law for the case of a well-known background; and, third, for large background, the expression has to be equivalent to those given by the three former models. It will be demonstrated that only the proposed model fulfills these requirements.