Revisiting Currie's Minimum Detectable Activity for Non-Destructive Assay By Gamma Detection Using Tolerance Intervals

Currie's paper [1] on estimating the minimum detectable activity (MDA) applied a Gaussian approximation to either Gaussian or Poisson data and remains the standard method to estimate radiological detection limits. This paper revisits the Currie method with attention to the false alarm probability (FAP) in Poisson and Gaussian data in non-destructive assay (NDA) by gamma (denoted asγ) detection. The Currie detection limit L_D is an estimate of the smallest net signal count rate λ_N that can be detected with high probability and low FAP in the presence of non-zero background count rate λ_B that has been previously estimated. The MDA is the sample activity or mass corresponding to λ_N, defined as MDA =L_D⁄ν, where in the case of γ-based NDA, the calibration factor n (a product of γ-ray yield, detector and geometric efficiency, counting time, and other factors) has measurement error that introduces systematic error in the estimate of the MDA. Kirkpatrick et al. [2] showed how to account for systematic uncertainties in the estimate of MDA =L_D⁄ν using a modified version of Currie estimation [2,3]. The present paper combines the approach in [2] with a tolerance interval approach. It is shown that the FAP in signal detection can be significantly different from the nominal FAP if the nominal FAP is not based on a tolerance interval, and if the nominal FAP is based on a tolerance interval, then the MDA will be larger than Currie's estimated MDA.