Calculation of decision thresholds according to the standard ISO 11929-3 in case of presence of the peaked background

Abstract

The method of calculation of the decision threshold with the Least Squares Method, described in the standard ISO 11929, is presented for the case when the sources of peaked background contribute to the peak holding the indication. The decision threshold is calculated from spectral data corresponding to the indication zero; therefore, the observed indication must be removed from the spectrum. When the peaked background is present, the indication completely overlaps with the peaked background, so it can't be unfolded directly. Therefore, two steps are needed in the calculation: the unfolding of the peak, housing the indication, from the continuous background and the possible overlapping peaks, and separating of the indication from the peaked background using the background data obtained from separate calculations and measurements. In this article it is shown that the method of least squares is flexible enough to accommodate all sources of uncertainty into the uncertainty matrix of input quantities. Its derivation is presented in detail and the calculation of the indication corresponding to the decision threshold is described. As a proof of the concept an example of calculating the number of counts corresponding to the decision threshold as a function of the indication is presented. The method of calculation and the results of the calculation are briefly discussed.