Calculation of the detection limit in radiation measurements with systematic uncertainties

The detection limit (L_D) or Minimum Detectable Activity (MDA) is an a priori evaluation of assay sensitivity intended to quantify the suitability of an instrument or measurement arrangement for the needs of a given application. Traditional approaches as pioneered by Currie rely on Gaussian approximations to yield simple, closed-form solutions, and neglect the effects of systematic uncertainties in the instrument calibration. These approximations are applicable over a wide range of applications, but are of limited use in low-count applications, when high confidence values are required, or when systematic uncertainties are significant. One proposed modification to the Currie formulation attempts account for systematic uncertainties within a Gaussian framework. We have previously shown that this approach results in an approximation formula that works best only for small values of the relative systematic uncertainty, for which the modification of Currie's method is the least necessary, and that it significantly overestimates the detection limit or gives infinite or otherwise non-physical results for larger systematic uncertainties where such a correction would be the most useful. We have developed an alternative approach for calculating detection limits based on realistic statistical modeling of the counting distributions which accurately represents statistical and systematic uncertainties. Instead of a closed form solution, numerical and iterative methods are used to evaluate the result. Accurate detection limits can be obtained by this method for the general case.