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.

Bayesian assessment of uncertainty in metrology: a tutorial

“…Insertion of equations ( 5) and ( 6) with p(D|π, A) = l(π; A, D) into equation ( 4 The results should correspond to those obtained by the propagation of distributions based on a Monte Carlo method as described in GUM S1, for details see e.g. [24,43,44]. However, the approach in GUM S1 is oriented mainly to measurement models having a single output quantity and consisting of a single equation.…”

“…Later, the procedure was succinctly outlined by Elster et al [4], who focused on its relation to the Monte Carlo method described in Supplement 1 to the GUM (GUM S1) [5] and by Wübeler et al [6], who explained the similarities and differences between the GUM and GUM S1 approaches. Several other papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and books [25][26][27][28] touch also on issues relevant to this general evaluation scheme.…”

Uncertainty, Detectability and Conformity in Measurements of Ionizing Radiation

“…If the GUM S1 is applied, numerical procedures are needed for the calculation of the limits of the coverage interval. 28) The decision rules 1-3 given above are substantiated in detail in Clauses 5.2 and 5.3.…”

Bayesian inference for measurements of ionizing radiation under partial information

“…Such issues do not fit well into the estimation theory of classical statistics. Bayesian inference, on the other hand, is well suited to take into account such information, and corresponding approaches have been proposed recently (see Weise et al (2006), Kirkpatrick and Young (2009), Weise et al (2009), Kirkpatrick et al (2013), Kirkpatrick and Young (2015) and Michel (2016), among others).…”