Decision threshold as a gauge of the measurement quality in gamma-ray spectrometric measurements

Abstract

We show that in gamma-ray spectrometric measurements the decision threshold depends on the observed value of the measurand. Since the decision threshold is intended to describe the sensitivity of the measurement, this dependence restricts its application to measurements where the indication is not expressive. To extend the direct applicability of the decision threshold to expressive indications in gamma-ray spectrometric measurements, where mainly the Region-of-Interest method is used to evaluate the isolated peaks, a recalculation of the decision thresholds to the peak widths corresponding to the inexpressive peaks is proposed. For the Least-Squares method, where the dependence of the decision threshold on the value of the measurand originates in the non-zero value of the correlation coefficient between the indication and the background, no recalculation is possible. Instead, we can only make a drastic simplification of the calculation, resulting in underestimated decision thresholds.

Keywords: Background; Indication; Least-squares method; Null-indication uncertainty; Region-of-Interest method; Variance-covariance matrix.