ISO/FDIS 11929-3

ISO /TC 85/SC 2
Secretariat: AFNOR
Date: 2025-06-18xx
Determination of the characteristic limits (decision threshold,
detection limit and limits of the coverage interval) for
measurements of ionizing radiation — Fundamentals and
applications — Part 3: Application to unfolding
methodsapplication —
Part 3:
Applications to unfolding methods
Détermination des limites caractéristiques (seuil de décision, limite de détection et extrémités de l'intervalle
élargi) pour mesurages de rayonnements ionisants — Principes fondamentaux et applications —
Partie 3: Applications aux méthodes de déconvolution
FDIS stage
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© ISO 2025 – All rights reserved
iii
Contents Page
Foreword . v
Introduction . vii
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Quantities and symbols . 6
5 Evaluation of a measurement using unfolding methods . 8
5.1 General aspects . 8
5.2 Models of unfolding and general uncertainty evaluation . 8
5.3 Unfolding as a sub-model . 10
5.4 Input quantities and their uncertainties . 11
5.5 Parameters of unfolding . 11
5.6 Procedure for unfolding . 12
5.7 Modification for Poisson distributed count numbers for unfolding . 15
5.8 Evaluation of the primary results and their associated standard uncertainties . 16
5.9 Standard uncertainty as a function of an assumed true value of the measurand . 16
5.10 Decision threshold, detection limit and assessments . 18
5.11 Coverage interval and the best estimate and its associated standard uncertainty . 19
5.12 Documentation . 20
Annex A (informative) Correlations and covariances . 22
Annex B (informative) Spectrum unfolding in nuclear spectrometric measurement . 26
Bibliography . 39

© ISO 2025 – All rights reserved
iv
Foreword
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This document was prepared by This document was prepared by ISO/TC 85, Nuclear energy, nuclear
technologies, and radiological protection, Subcommittee SC 2, Radiological protection, in collaboration with the
European Committee for Standardization (CEN) Technical Committee CEN/TC 430, Nuclear energy, nuclear
technologies, and radiological protection, in accordance with the Agreement on technical cooperation between
ISO and CEN (Vienna Agreement).
This third edition of ISO 11929-3 replaces ISO 11929-3:2019, of which it constitutes a minor revision.
The main changes are as follows:
— — general : to correctcorrection of the internal references within the text;
— — 3.12 and 3.13 : correction of the definitiondefinitions of decision threshold (3.12) and the detection
limit (3.13);
— — 4 : to correctcorrection of 4 according to comments;
— — B.2 : correction of 0Formulae (B.2) and 0(B.4);
th
— — B.3.2 : correction of the 8 paragraph in B.3.2;
st
— — B.3.5 : correction of the 1rst1 paragraph B.3.5;
th
— — B.5.2 : correction of the 7 paragraph B.5.2.
© ISO 2025 – All rights reserved
v
A list of all the parts in the ISO 11929 series can be found on the ISO website.
© ISO 2025 – All rights reserved
vi
Introduction
Measurement uncertainties and characteristic values, such as the decision threshold, the detection limit and
limits of the coverage interval for measurements as well as the best estimate and its associated standard
measurement uncertainty, are of importance in metrology in general and for radiological protection in
particular. The quantification of the uncertainty associated with a measurement result provides a basis for the
trust an individual can have in a measurement result. Conformity with regulatory limits, constraints or
reference values can only be demonstrated by taking into account and quantifying all sources of uncertainty.
Characteristic limits provide, at the end, the basis for deciding under uncertainty.
This standard provides characteristic values of a non-negative measurand of ionizing radiation. It is also
applicable for a wide range of measuring methods extending beyond measurements of ionizing radiation.
The limits to be provided according to the ISO 11929 series for specified probabilities of wrong decisions allow
detection possibilities to be assessed for a measurand and for the physical effect quantified by this measurand
as follows:
— — the “decision threshold” allows a decision to be made on whether or not the physical effect quantified
by the measurand is present;
— — the “detection limit” indicates the smallest true quantity value of the measurand that can still be
detected with the applied measurement procedure; this gives a decision on whether or not the
measurement procedure satisfies the requirements and is therefore suitable for the intended
measurement purpose;
— — the “limits of the coverage interval” enclose, in the case of the physical effect recognized as present, a
coverage interval containing the true quantity value of the measurand with a specified probability.
Hereinafter, the limits mentioned are jointly called the “characteristic limits”.
NOTE According to ISO/IEC Guide 99:2007 updated by JCGM 200:2012 the term “coverage interval” is used here
instead of “confidence interval” in order to distinguish the wording of Bayesian terminology from that of conventional
statistics.
All the characteristic values are based on Bayesian statistics and on the ISO/IEC 98-3 Guide to the Expression
of Uncertainty in Measurement as well as on the ISO/IEC Guide 98-3:2008/Suppl 1:2008 and ISO/IEC Guide
98-3:2008/Suppl 2:2011. As explained in detail in ISO 11929-2, the characteristic values are mathematically
defined by means of moments and quantiles of probability distributions of the possible measurand values.
Since measurement uncertainty plays an important part in ISO 11929, the evaluation of measurements and
the treatment of measurement uncertainties are carried out by means of the general procedures according to
the ISO/IEC Guide 98-3 and to the ISO/IEC Guide 98-3:2008/Suppl 1:2008; see also References [0[9]] to
[0[13]] This enables the strict separation of the evaluation of the measurements, on the one hand, and the
provision and calculation of the characteristic values, on the other hand. The ISO 11929 series makes use of a
[ [14]] to[ [16]]
theory of uncertainty in measurement 0 0 based on Bayesian statistics (e.g. References [0.[17]] to
[0[22])]) in order to allow to take into account also those uncertainties that cannot be derived from repeated
or counting measurements. The latter uncertainties cannot be handled by frequentist statistics.
Because of developments in metrology concerning measurement uncertainty laid down in the
ISO/IEC Guide 98-3, ISO 11929:2010 was drawn up on the basis of the ISO/IEC Guide 98-3, but using Bayesian
statistics and the Bayesian theory of measurement uncertainty. This theory provides a Bayesian foundation
for the ISO/IEC Guide 98-3. Moreover, ISO 11929:2010 was based on the definitions of the characteristic
[ [9] ] [ [10] ] [ [11] ]
values 0 , , the standard proposal 0 , , and the introducing article 0 . . It unified and replaced all earlier
parts of ISO 11929 and was applicable not only to a large variety of particular measurements of ionizing
radiation but also, in analogy, to other measurement procedures.
© ISO 2025 – All rights reserved
vii
Since the ISO/IEC Guide 98-3:2008/Suppl 1:2008 has been published, dealing comprehensively with a more
general treatment of measurement uncertainty using the Monte Carlo method in complex measurement
[ [12]]
evaluations. This provided an incentive for writing a corresponding Monte Carlo supplement 0 to
ISO 11929:2010 and to revise ISO 11929:2010. The revised ISO 11929 is also essentially founded on Bayesian
statistics and can serve as a bridge between ISO 11929:2010 and the ISO/IEC Guide 98-3:2008/Suppl 1:2008.
Moreover, more general definitions of the characteristic values (ISO 11929-2) and the Monte Carlo
computation of the characteristic values make it possible to go a step beyond the present state of
standardization laid down in ISO 11929:2010 since probability distributions rather than uncertainties can be
propagated. It is thus more comprehensive and extending the range of applications.
The revised ISO 11929, moreover, is more explicit on the calculation of the characteristic values. It corrects
also a problem in ISO 11929:2010 regarding uncertain quantities and influences, which do not behave
randomly in measurements repeated several times. Reference [0[13]] gives a survey on the basis of the
revision. Furthermore, this document gives detailed advice how to calculate characteristic values in the case
of multivariate measurements using unfolding methods. For such measurements, the ISO/IEC Guide 98-
3:2008/Suppl 2:2011 provides the basis of the uncertainty evaluation.
Formulas are provided for the calculation of the characteristic values of an ionizing radiation measurand via
the “standard measurement uncertainty” of the measurand (hereinafter the “standard uncertainty”) derived
according to the ISO/IEC Guide 98-3 as well as via probability density functions (PDFs) of the measurand
derived in accordance with ISO/IEC Guide 98-3:2008/Suppl 1:2008. The standard uncertaintie
...