Monte Carlo determination of the characteristic limits in measurement of ionising radiation--fundamentals and numerics

Abstract

It is shown how the decision threshold, the detection limit and the limits of a coverage interval - summarily called the characteristic limits - and, in addition, the best estimate and the associated standard uncertainty of a non-negative radiation measurand are to be calculated by using the Monte Carlo (MC) method in ionising-radiation measurements. The limits are mathematically defined by means of quantiles of the Bayesian distributions of the possible measurand values. The MC-induced uncertainties of the limits and typical problems connected with MC application are also treated. The paper can serve as a bridge between the ISO Guide to the Expression of Uncertainty in Measurement (GUM), Supplement 1 applying the MC method and ISO/FDIS 11929 (at present in preparation) dealing with the characteristic limits. As an illustration, a net count rate measurand, being the difference of a gross and a background count rate, is treated theoretically and numerically. More complex examples deal with the wipe test for surface contamination and with a linear multi-channel spectrum unfolding.