Optimization of the decision threshold for single radioactive counting

When the activity of a sample is close to the background level, the decision threshold is classically defined by considering distributions of sample and background as being equal. Recently, the Bayesian approach has been considered in the standard ISO to refine the determination of the decision threshold by taking into account all accessible information prior to measurement such as type A and type B uncertainties. However, simplifications using Gaussian approximation and experimental values instead of true means are often used to facilitate calculations. In this paper, we develop a complete treatment without simplification, based on the Bayesian approach and Poisson distribution. Minimal informations have been considered: one single raw counting for the sample and one previously acquired background. From one single background counting, the net background probability law is calculated and then a decision threshold is deduced. In particular, we demonstrate that the decision threshold is defined for any case including very low background or even null event. Comparisons with classical approach as well as the Bayesian treatment in the new ISO 11929 have been carried out. Applications of this decision threshold for the optimisation of radioactive measurement or in case of a set of minimal detectable activities used to determine average releases are given. Bayesian treatment also gives relevant informations such as the probability for a source to be radioactive when the net number of counts is below the decision threshold.