EN ISO 11929-2:2025

Determination of the characteristic limits (decision threshold, detection limit and limits of the coverage interval) for measurements of ionizing radiation - Fundamentals and application - Part 2: Advanced applications (ISO 11929-2:2025)

The ISO 11929 series specifies a procedure, in the field of ionizing radiation metrology, for the calculation of the “decision threshold”, the “detection limit” and the “limits of the coverage interval” for a non-negative ionizing radiation measurand when counting measurements with preselection of time or counts are carried out. The measurand results from a gross count rate and a background count rate as well as from further quantities on the basis of a model of the evaluation. In particular, the measurand can be the net count rate as the difference of the gross count rate and the background count rate, or the net activity of a sample. It can also be influenced by calibration of the measuring system, by sample treatment and by other factors.
ISO 11929 has been divided into four parts covering elementary applications in ISO 11929-1, advanced applications on the basis of the GUM Supplement 1 in this document, applications to unfolding methods in ISO 11929-3, and guidance to the application in ISO 11929-4.
ISO 11929-1 covers basic applications of counting measurements frequently used in the field of ionizing radiation metrology. It is restricted to applications for which the uncertainties can be evaluated on the basis of the ISO/IEC Guide 98-3 (JCGM 2008). In ISO 11929-1:2025, Annex A, the special case of repeated counting measurements with random influences is covered, while measurements with linear analogous ratemeters are covered in ISO 11929-1:2025, Annex B.
ISO 11929-3 deals with the evaluation of measurements using unfolding methods and counting spectrometric multi-channel measurements if evaluated by unfolding methods, in particular, for alpha- and gamma‑spectrometric measurements. Further, it provides some advice on how to deal with correlations and covariances.
ISO 11929-4 gives guidance to the application of ISO 11929, summarizes shortly the general procedure and then presents a wide range of numerical examples. Information on the statistical roots of ISO 11929 and on its current development may be found elsewhere[30][31].
ISO 11929 also applies analogously to other measurements of any kind especially if a similar model of the evaluation is involved. Further practical examples can be found, for example, in ISO 18589[1], ISO 9696[2], ISO 9697[3], ISO 9698[4], ISO 10703[5], ISO 7503[6], ISO 28218[7] and ISO 11665[8].
NOTE            A code system, named UncertRadio, is available for calculations according to ISO 119291 to ISO 11929-3. UncertRadio[27][28] can be downloaded for free from https://www.thuenen.de/en/institutes/fisheries-ecology/fields-of-activity/marine-environment/coordination-centre-of-radioactivity/uncertradio. The download contains a setup installation file which copies all files and folders into a folder specified by the user. After installation one has to add information to the PATH of Windows as indicated by a pop‑up window during installation. English language can be chosen and extensive “help” information is available. Another tool is the package ‘metRology’[32] which is available for programming in R. It contains the two R functions ‘uncert’ and ‘uncertMC’ which perform the GUM conform uncertainty propagation, either analytically or by the Monte Carlo method, respectively. Covariances/correlations of input quantities are included. Applying these two functions within iterations for decision threshold and the detection limit calculations simplifies the programming effort significantly. It is also possible to imp

Bestimmung der charakteristischen Grenzen (Erkennungsgrenze, Nachweisgrenze und Grenzen des Überdeckungsintervalls) bei Messungen ionisierender Strahlung - Grundlagen und Anwendungen - Teil 2: Fortgeschrittene Anwendungen (ISO/FDIS 11929-2:2025)

Détermination des limites caractéristiques (seuil de décision, limite de détection et limites de l’intervalle élargi) pour mesurages de rayonnements ionisants - Principes fondamentaux et applications - Partie 2: Applications avancées (ISO 11929-2:2025)

La série ISO 11929 spécifie une procédure applicable, dans le domaine de la métrologie des rayonnements ionisants, pour le calcul du «seuil de décision», de la «limite de détection» et des «limites de l’intervalle élargi» pour un mesurande de rayonnement ionisant non négatif, lorsque des mesurages par comptage sont effectués avec une présélection du temps ou du nombre d’impulsions. Le mesurande résulte d’un taux de comptage brut et d’un taux de comptage du bruit de fond ainsi que de grandeurs supplémentaires reposant sur un modèle d’évaluation. En particulier, le mesurande peut être le taux de comptage net défini comme la différence du taux de comptage brut et du taux de comptage du bruit de fond, ou l’activité nette d’un échantillon. Il peut également être influencé par l’étalonnage du système de mesure, par le traitement de l’échantillon et par d’autres facteurs.
L’ISO 11929 a été scindée en quatre parties couvrant les applications élémentaires dans l’ISO 11929-1, les applications avancées reposant sur le Supplément 1 du GUM dans le présent document, les applications aux méthodes de déconvolution dans l’ISO 11929-3, et les recommandations d’application dans l’ISO 11929-4.
L’ISO 11929-1 couvre les applications de base des mesurages par comptage souvent utilisées dans le domaine de la métrologie des rayonnements ionisants. Elle se limite aux applications pour lesquelles il est possible d’évaluer les incertitudes sur la base du Guide ISO/IEC 98-3 (JCGM 2008). L’ISO 11929-1:2025, Annexe A, traite du cas particulier des mesurages répétés par comptage avec des influences aléatoires, alors que l’ISO 11929-1:2025, Annexe B, couvre les mesurages avec des ictomètres analogiques linéaires.
L’ISO 11929-3 traite de l’évaluation des mesurages en utilisant des méthodes de déconvolution ainsi que de l’évaluation des mesurages multicanaux spectrométriques par comptage en cas d’évaluation par des méthodes de déconvolution, en particulier pour les mesurages spectrométriques alpha et gamma. Elle fournit en outre des conseils pour le traitement avec des corrélations et des covariances.
L’ISO 11929-4 fournit des recommandations pour l’application de l’ISO 11929, résume les grandes lignes de la procédure générale et présente ensuite un large éventail d’exemples numériques. Des informations relatives à l’origine des statistiques de l’ISO 11929 et à son stade de développement actuel peuvent être trouvées dans les Références [29] et [30].
L’ISO 11929 s’applique également de manière analogue à d’autres mesurages de tout type, notamment si un modèle d’évaluation similaire est concerné. D’autres exemples pratiques sont, par exemple, disponibles dans l’ISO 18589[1], l’ISO 9696[2], l’ISO 9697[3], l’ISO 9698[4], l’ISO 10703[5], l’ISO 7503[6], l’ISO 28218[7] et l’ISO 11665[8].
NOTE            Un logiciel, baptisé UncertRadio, est disponible pour les calculs conformément aux ISO 11929 1 à 11929-3. UncertRadio[27][28] peut être téléchargé gratuitement à l’adresse: https://www.thuenen.de/en/institutes/fisheries-ecology/fields-of-activity/marine-environment/coordination-centre-of-radioactivity/uncertradio. Le logiciel disponible en téléchargement contient un fichier d’installation qui copie tous les fichiers et dossiers à un emplacement spécifié par l’utilisateur. Après l’installation, des informations doivent être saisies concernant le CHEMIN sous Windows qui a été indiqué dans une fenêtre contextuelle au cours de l’installation. La langue anglaise peut être choisie et

Ugotavljanje karakterističnih mej (odločitveni prag, zaznavanje meje in omejitev intervala pokritja) pri meritvah ionizirnega sevanja - Osnove in uporaba - 2. del: Napredne aplikacije (ISO/FDIS 11929-2:2025)

General Information

• Status: Published
• Publication Date: 16-Dec-2025
• ICS: 17.240 - Radiation measurements
• Technical Committee: CEN/TC 430 - Nuclear energy, nuclear technologies, and radiological protection
• Drafting Committee: CEN/TC 430 - Nuclear energy, nuclear technologies, and radiological protection
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 17-Dec-2025
• Completion Date: 17-Dec-2025
• Ref Project: oSIST prEN ISO 11929-2:2025 - Determination of the characteristic limits (decision threshold, detection limit and limits of the coverage interval) for measurements of ionizing radiation - Fundamentals and application - Part 2: Advanced applications (ISO/FDIS 11929-2:2025)

Relations

• Replaces: EN ISO 11929-2:2021 - Determination of the characteristics limits (decision threshold, detection limit and limits of the coverage interval) for measurements of ionizing radiation - Fundamentals and application - Part 2: Advanced applications (ISO 11929-2:2019)
• Effective Date: 13-Nov-2024

Standards Content (Sample)

SLOVENSKI STANDARD
01-oktober-2025
Ugotavljanje karakterističnih mej (odločitveni prag, zaznavanje meje in omejitev
intervala pokritja) pri meritvah ionizirnega sevanja - Osnove in uporaba - 2. del:
Napredne aplikacije (ISO/FDIS 11929-2:2025)
Determination of the characteristic limits (decision threshold, detection limit and limits of
the coverage interval) for measurements of ionizing radiation - Fundamentals and
application - Part 2: Advanced applications (ISO/FDIS 11929-2:2025)
Bestimmung der charakteristischen Grenzen (Erkennungsgrenze, Nachweisgrenze und
Grenzen des Überdeckungsintervalls) bei Messungen ionisierender Strahlung -
Grundlagen und Anwendungen - Teil 2: Fortgeschrittene Anwendungen (ISO/FDIS
11929-2:2025)
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 2: Applications avancées (ISO/FDIS 11929-
2:2025)
Ta slovenski standard je istoveten z: prEN ISO 11929-2
ICS:
17.240 Merjenje sevanja Radiation measurements
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

FINAL DRAFT
International
Standard
ISO/FDIS 11929-2
ISO/TC 85/SC 2
Determination of the characteristic
Secretariat: AFNOR
limits (decision threshold, detection
Voting begins on:
limit and limits of the coverage
interval) for measurements of
Voting terminates on:
ionizing radiation — Fundamentals
and application —
Part 2:
Advanced applications
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 2: Applications avancées
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
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INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
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MADE IN NATIONAL REGULATIONS.
Reference number
ISO/FDIS 11929-2:2025(en) © ISO 2025

FINAL DRAFT
ISO/FDIS 11929-2:2025(en)
International
Standard
ISO/FDIS 11929-2
ISO/TC 85/SC 2
Determination of the characteristic
Secretariat: AFNOR
limits (decision threshold, detection
Voting begins on:
limit and limits of the coverage
interval) for measurements of
Voting terminates on:
ionizing radiation — Fundamentals
and application —
Part 2:
Advanced applications
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 2: Applications avancées
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2025
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/CEN PARALLEL PROCESSING
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
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ISO copyright office
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Published in Switzerland Reference number
ISO/FDIS 11929-2:2025(en) © ISO 2025

ii
ISO/FDIS 11929-2:2025(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Quantities and symbols . 6
5 Summary of procedures for evaluating and reporting uncertainty and characteristic
limits . 8
6 Evaluation of a measurement on the basis of ISO/IEC Guide 98-3:2008/Suppl 1:2008 .11
6.1 Introduction and decisions to be made .11
6.2 General aspects concerning the measurand and the model of evaluation .11
6.3 Establishing probability distributions for the input quantities . 12
6.4 Propagating probability distributions .14
6.5 Evaluation of the primary measurement result . 15
6.6 Standard uncertainty associated with the primary measurement result . 15
7 PDF for an assumed true value of the measurand .15
8 Decision threshold, detection limit and assessments .16
8.1 Specifications .16
8.2 Decision threshold .16
8.3 Detection limit .17
8.4 Assessments . .18
9 Limits of the coverage interval .18
9.1 General Aspects .18
9.2 The probabilistically symmetric coverage interval .19
9.3 The shortest coverage interval .19
10 The best estimate and its associated standard uncertainty .20
11 Documentation .20
Annex A (normative) Measurements with low count numbers .22
Annex B (informative) Explanatory notes .24
Bibliography .38

iii
ISO/FDIS 11929-2:2025(en)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
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 11929-2 replaces ISO 11929-2:2019, of which it constitutes a minor revision.
The main changes are as follows:
— correction of the internal references within the text;
— correction of the definitions of decision threshold (3.12) and the detection limit (3.13);
— editorial correction in Clause 7;
— correction of Formula (B.3);
— correction of Formula (B.17);
— correction of Formula (B.27);
— editorial correction in B.4.
A list of all the parts in the ISO 11929 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
ISO/FDIS 11929-2:2025(en)
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 – in the end – the basis for deciding under uncertainty.
The ISO 11929 series 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 the ISO 11929 series, 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 [9] to [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
[14 to 16]
makes use of a theory of uncertainty in measurement based on Bayesian statistics (e.g. References
[17] to [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, the standard proposal, and the introducing article. 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.
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 to
ISO 11929:2010 and to revise ISO 11929:2010. The revised ISO 11929 is also essentially founded on

v
ISO/FDIS 11929-2:2025(en)
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 ISO 11929 series, 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 [13] gives a survey on the basis of the revision.
ISO 11929-2 extends the scope of ISO 11929:2010 whereas ISO 11929-1 replaces the former. Furthermore,
in ISO 11929-3, it 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 distributions of the measurand derived
in accordance with ISO/IEC Guide 98-3:2008/Suppl 1:2008. The standard uncertainties or probability
distributions take into account the uncertainties of the actual measurement as well as those of sample
treatment, calibration of the measuring system and other influences. The latter uncertainties are assumed
to be known from previous investigations.

vi
FINAL DRAFT International Standard ISO/FDIS 11929-2:2025(en)
Determination of the characteristic limits (decision
threshold, detection limit and limits of the coverage interval)
for measurements of ionizing radiation — Fundamentals and
application —
Part 2:
Advanced applications
1 Scope
The ISO 11929 series specifies a procedure, in the field of ionizing radiation metrology, for the calculation
of the “decision threshold”, the “detection limit” and the “limits of the coverage interval” for a non-negative
ionizing radiation measurand when counting measurements with preselection of time or counts are carried
out. The measurand results from a gross count rate and a background count rate as well as from further
quantities on the basis of a model of the evaluation. In particular, the measurand can be the net count rate
as the difference of the gross count rate and the background count rate, or the net activity of a sample. It can
also be influenced by calibration of the measuring system, by sample treatment and by other factors.
ISO 11929 has been divided into four parts covering elementary applications in ISO 11929-1, advanced
applications on the basis of the GUM Supplement 1 in this document, applications to unfolding methods in
ISO 11929-3, and guidance to the application in ISO 11929-4.
ISO 11929-1 covers basic applications of counting measurements frequently used in the field of ionizing
radiation metrology. It is restricted to applications for which the uncertainties can be evaluated on the basis
of the ISO/IEC Guide 98-3 (JCGM 2008). In ISO 11929-1:—, Annex A, the special case of repeated counting
measurements with random influences is covered, while measurements with linear analogous ratemeters
are covered in ISO 11929-1:—, Annex B.
ISO 11929-3 deals with the evaluation of measurements using unfolding methods and counting
spectrometric multi-channel measurements if evaluated by unfolding methods, in particular, for alpha- and
gamma-spectrometric measurements. Further, it provides some advice on how to deal with correlations and
covariances.
ISO 11929-4 gives guidance to the application of ISO 11929, summarizes shortly the general procedure and
then presents a wide range of numerical examples. Information on the statistical roots of ISO 11929 and on
[30][31]
its current development may be found elsewhere .
ISO 11929 also applies analogously to other measurements of any kind especially if a similar model of the
[1] [2]
evaluation is involved. Further practical examples can be found, for example, in ISO 18589 , ISO 9696 ,
[3] [4] [5] [6] [7] [8]
ISO 9697 , ISO 9698 , ISO 10703 , ISO 7503 , ISO 28218 and ISO 11665 .
NOTE A code system, named UncertRadio, is available for calculations according to ISO 119291 to ISO 11929-3.
[27][28]
UncertRadio can be downloaded for free from https:// www .thuenen .de/ en/ institutes/ fisheries -ecology/ fields
-of -activity/ marine -environment/ coordination -centre -of -radioactivity/ uncertradio. The download contains a setup
installation file which copies all files and folders into a folder specified by the user. After installation one has to add
information to the PATH of Windows as indicated by a pop-up window during installation. English language can be
[32]
chosen and extensive “help” information is available. Another tool is the package ‘metRology’ which is available
for programming in R. It contains the two R functions ‘uncert’ and ‘uncertMC’ which perform the GUM conform
uncertainty propagation, either analytically or by the Monte Carlo method, respectively. Covariances/correlations of
input quantities are included. Applying these two functions within iterations for decision threshold and the detection
limit calculations simplifies the programming effort significantly. It is also possible to implement this document in a
spreadsheet containing a Monte Carlo add-in or into other commercial mathematics software.

ISO/FDIS 11929-2:2025(en)
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 80000-1, Quantities and units — Part 1: General
ISO 80000-10, Quantities and units — Part 10: Atomic and nuclear physics
ISO/IEC Guide 98-3, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in
measurement (GUM:1995)
ISO/IEC Guide 98-3:2008/Suppl 1:2008, Evaluation of measurement data — Supplement 1 to the “Guide to the
expression of uncertainty in measurement” — a Propagation of distributions using a Monte Carlo method, JCGM
101:2008
ISO/IEC Guide 98-3:2008/Suppl 2:2011, Evaluation of measurement data — Supplement 2 to the “Guide to the
expression of uncertainty in measurement” — Models with any number of output quantities, JCGM 102:2011
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated terms (VIM)
3 Terms and definitions
For the purposes of the ISO 11929 series, the terms and definitions given in ISO 80000-1, ISO 80000-10,
ISO/IEC Guide 98-3, ISO/IEC Guide 98-3:2008/Suppl 1:2008, ISO/IEC Guide 98-3:2008/Suppl 2:2011,
ISO/IEC Guide 99 and ISO 3534-1 and the following apply.
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
[SOURCE: JCGM 200:2012, 1.19]
3.2
measurement
process of experimentally obtaining one or more quantity values that can reasonably be attributed to a
quantity
[SOURCE: JCGM 200:2012, 2.1]
3.3
measurand
quantity intended to be measured
[SOURCE: JCGM 200:2012, 2.3]
ISO/FDIS 11929-2:2025(en)
3.4
coverage interval
interval containing the set of true quantity values of a measurand with a stated probability, based on the
information available
[SOURCE: JCGM 200:2012, 2.36]
Note 1 to entry: A coverage interval does not need to be centred on the chosen measured quantity value (see
JCGM 101:2008).
Note 2 to entry: A coverage interval should not be termed “confidence interval” to avoid confusion with the statistical
concept.
3.5
measurement method
method of measurement
generic description of a logical organization of operations used in a measurement
[SOURCE: JCGM 200:2012, 2.5]
3.6
measurement procedure
detailed description of a measurement according to one or more measurement principles and to a
given measurement method, based on a measurement model and including any calculation to obtain a
measurement result
[SOURCE: JCGM 200:2012, 2.6]
3.7
measurement result
result of measurement
set of quantity values being attributed to a measurand together with any other available relevant information
[SOURCE: JCGM 200:2012, 2.9]
3.8
measured quantity value
value of a measured quantity
measured value
quantity value representing a measurement result
[SOURCE: JCGM 200:2012, 2.10]
3.9
true quantity value
true value of a quantity
true value
quantity value consistent with the definition of a quantity
[SOURCE: JCGM 200:2012, 2.11]
Note 1 to entry: In the Error Approach to describing measurement, a true quantity value is considered unique and, in
practice, unknowable. The Uncertainty Approach is to recognize that, owing to the inherently incomplete amount of
detail in the definition of a quantity, there is not a single true quantity value but rather a set of true quantity values
consistent with the definition. However, this set of values is, in principle and in practice, unknowable. Other approaches
dispense altogether with the concept of true quantity value and rely on the concept of metrological compatibility of
measurement results for assessing their validity.
Note 2 to entry: When the definitional uncertainty associated with the measurand is considered to be negligible
compared to the other components of the measurement uncertainty, the measurand may be considered to have
an “essentially unique” true quantity value. This is the approach taken by the ISO/IEC Guide 98-3 and associated
documents, where the word “true” is considered to be redundant.

ISO/FDIS 11929-2:2025(en)
3.10
measurement uncertainty
uncertainty of measurement
uncertainty
non-negative parameter characterizing the dispersion of the quantity values being attributed to a
measurand, based on the information used
[SOURCE: JCGM 200:2012, 2.26]
Note 1 to entry: Measurement uncertainty includes components arising from systematic effects, such as components
associated with corrections and the assigned quantity values of measurement standards, as well as the definitional
uncertainty. Sometimes estimated systematic effects are not corrected for but, instead, associated measurement
uncertainty components are incorporated.
Note 2 to entry: The parameter may be, for example, a standard deviation called standard measurement uncertainty
(or a specified multiple of it), or the half-width of an interval, having a stated coverage probability.
Note 3 to entry: Measurement uncertainty comprises, in general, many components. Some of these may be evaluated
by Type A evaluation of measurement uncertainty from the statistical distribution of the quantity values from series
of measurements and can be characterized by standard deviations. The other components, which may be evaluated
by Type B evaluation of measurement uncertainty, can also be characterized by standard deviations, evaluated from
probability distribution based on experience or other information.
Note 4 to entry: In general, for a given set of information, it is understood that the measurement uncertainty is
associated with a stated quantity value attributed to the measurand. A modification of this value results in a
modification of the associated uncertainty.
3.11
model of evaluation
set of mathematical relationships between all measured and other quantities involved in the evaluation of
measurements
Note 1 to entry: The model of evaluation does not need to be an explicit function; it can also be an algorithm realized
by a computer code.
3.12
decision threshold
value of the estimator of the measurand, which when exceeded by the result of an actual measurement using
a given measurement procedure of a measurand quantifying a physical effect, is used to decide that the
physical effect is present
Note 1 to entry: In cases where the measurement result, y, exceeds the decision threshold, y*, it is decided to conclude
that the physical effect is present. The probability of making an erroneous decision in this case is equal to the pre-
selected probability α. An incorrect decision means assuming a physical effect, even though it is, in fact, absent.
Note 2 to entry: If the result, y, is below the decision threshold, y * , it is decided to conclude that the result cannot be
attributed to the physical effect; nevertheless it cannot be concluded that it is absent.
Note 3 to entry: The probability α is the probability that a measured value exceeds the decision threshold and is
accepted as indicator for a non-zero true value although it is, in fact, zero. In this case, the conclusion ỹ > 0 would be a
wrong decision.
Note 4 to entry: The probability β is hereby the probability that a measured value lies below the decision threshold
#
and the result is therefore not attributed to the physical effect although the true value equals the detection limit y . In
this case, the conclusion ỹ = 0 would be a wrong decision.

ISO/FDIS 11929-2:2025(en)
3.13
detection limit
smallest true value of the measurand which ensures a specified probability of being detectable by the
measurement procedure
#
Note 1 to entry: The detection limit, y , is the smallest true value for which the probability that the measured value-y
falls below the decision threshold according to 3.12 is the pre-selected probability β. If a measured value falls below the
decision threshold, it is decided to conclude that there is no physical effect, although, in fact it exists. This would result in
a wrong decision being made with the probability β. The probability of making the correct decision is consequently (1-β).
Note 2 to entry: The terms detection limit and decision threshold are used in an ambiguous way in different standards
(e.g. standards related to chemical analysis or quality assurance). If these terms are referred to one has to state
according to which standard they are used.
3.14
probabilistically symmetric coverage interval
coverage interval for a quantity such that the probability that the quantity is less than the smallest value in
the interval is equal to the probability that the quantity is greater than the largest value in the interval
[SOURCE: JCGM 101:2008, 3.15]
3.15
shortest coverage interval
coverage interval for a quantity with the shortest length among all coverage intervals for that quantity
having the same coverage probability
[SOURCE: JCGM 101:2008, 3.16]
3.16
limits of the coverage interval
values which define a coverage interval
Note 1 to entry: The limits are calculated in the ISO 11929 series to contain the true value of the measurand with a
specified probability 1−γ .
()
Note 2 to entry: The definition of a coverage interval is ambiguous without further stipulations. In this standard two
alternatives, namely the probabilistically symmetric and the shortest coverage interval are used.
3.17
best estimate of the true quantity value of the measurand
expectation value of the probability distribution of the true quantity value of the measurand, given the
experimental result and all prior information on the measurand
Note 1 to entry: The best estimate is the one among all possible estimates of the measurand on the basis of given
information, which is associated with the minimum uncertainty.
3.18
guideline value
value which corresponds to scientific, legal or other requirements with regard to the detection capability
and which is intended to be assessed by the measurement procedure by comparison with the detection limit
Note 1 to entry: The guideline value can be given, for example, as an activity, a specific activity or an activity
concentration, a surface activity or a dose rate.
Note 2 to entry: The comparison of the detection limit with a guideline value allows a decision on whether or not
the measurement procedure satisfies the requirements set forth by the guideline value and is therefore suitable for
the intended measurement purpose. The measurement procedure satisfies the requirement if the detection limit is
smaller than the guideline value.
Note 3 to entry: The guideline value shall not be confused with other values stipulated as conformity requests or as
regulatory limits.
ISO/FDIS 11929-2:2025(en)
3.19
background effect
measurement effect caused by radiation other than that caused by the object of the measurement itself
Note 1 to entry: The background effect can be due to natural radiation sources or radioactive materials in or around
the measuring instrumentation and also to the sample itself (for instance, from other lines in a spectrum).
3.20
background effect in spectrometric measurement
number of events of no interest in the region of a specific line in the spectrum
3.21
net effect
contribution of the possible radiation of a measurement object (for instance, of a radiation source or radiation
field) to the measurement effect
3.22
gross effect
measurement effect caused by the background effect and the net effect
3.23
shielding factor
factor describing the reduction of the background count rate by the effect of shielding caused by the
measurement object
3.24
relaxation time constant
duration in which the output signal of a linear-scale ratemeter decreases to 1/e times the starting value
after stopping the sequence of the input pulses
4 Quantities and symbols
The symbols for auxiliary quantities and the symbols only used in the annexes are not listed. Physical
quantities are denoted by upper-case letters but shall be carefully distinguished from their values, denoted
by the corresponding lower-case letters.
m number of input quantities
n number of Monte Carlo trials performed
M
X input quantity im=1,.,
()
i
x estimate of the input quantity X
i i

x possible true quantity values of the input quantity X
i i
xx,., drawing set of xx,., from the i-th Monte Carlo trial
1,in,i 1 n
ξ integration variable of possible true quantity values of the input quantity X
i i
ux() standard uncertainty of the input quantity X associated with the estimate x
i i i
Δx width of the region of the possible values of the input quantity X
i i
relative standard uncertainty of a quantity W associated with the estimate w
uw
()
rel
G model function
ISO/FDIS 11929-2:2025(en)
Y non-negative measurand, which quantifies the physical effect of interest; also used as
the symbol for a random variable as an estimator of the measurand
Y random variable used as an estimator of the measurand which does not take into account
that the measurand is non-negative

y
possible or assumed true values of the measurand; if the physical effect of interest is
not present, then y =0; otherwise, y > 0
η
integration variable of possible true quantity values of the output quantity Y
y determined value of the estimator Y, estimate of the measurand, primary measurement
result of the measurand
′
y variable describing possible measurement results (estimates)
y values y from different measurements j =0,1,2,.
()
j

vector of results from n Monte Carlo trials
yy= ,.,y M
{}
Mn1
M
uy
() standard uncertainty of the measurand associated with the primary measurement result y

 standard uncertainty of the estimator Y as a function of an assumed true value y of the
uy()
measurand

fy()y probability distribution; i.e. the conditional probability distribution of estimates, y, given
Y

an assumed true value, y , of the measurand, Y
probability distributions of the possible true values, y , of the measurand, Y, given the
fy y
()
Y
measured estimate, y (Bayesian statistics)
probability distribution of the possible true value, y , of the measurand, Y, given a set of
fy() a
Y
information a about the input quantities and their values and relations to the output
quantity
fy model prior; it represents all the information about the measurand available before the
()
Y
experiment is performed
 
Fy()a distribution function of the probability distribution fy()a
Y Y
Hx() 0 x< 0
 
Heaviside step function: fx()= for
 
H
1 x≥ 0
 
 
Ga(;rn,/1 t) Gamma function as the probability density function (PDF) of the true value r of a count
rate R given n counts obtained during a counting time t
Nx ,ux Normal or Gaussian distribution with the parameters x and ux
()() ()
Rx(,x ) Rectangular distribution with the lower and upper limits x and x
L U L U
Ef()()x expectation of fx()
X X
Var()fx() variance of fx()
X X
a
sets of information regarding the input quantities, respectively, including their values
and relations
ISO/FDIS 11929-2:2025(en)
a′
modified sets of information regarding the input quantities, respectively, including their
values and relations
ˆ
y best estimate of the measurand
standard uncertainty of the measurand associated with the best estimate ˆy
uyˆ
()
y *
decision threshold of the measurand
#
detection limit of the measurand
y
y guideline value of the measurand
r
 
lower and upper limit of the symmetric coverage interval, respectively, of the measurand
y , y
< >
lower and upper limit of the shortest coverage interval, respectively, of the measurand
y , y
R count rate as an input quantity X
i i
R count rate of the net effect (net count rate)
n
R count rate of the gross effect (gross count rate)
g
R count rate of the background effect (background count rate)
r , r estimate of the gross count rate and of the background count rate, respectively
g 0
ρρ, integration variables of possible true quantity values of the gross and background count
g 0
rates RR,
g 0
n number of counted pulses obtained from the measurement of the count rate R
i i
n , n number of counted pulses of the gross effect and of the background effect, respectively
g 0
t measurement duration of the measurement of the count rate R
i i
t , t measurement duration of the measurement of the gross effect and of the background
g 0
effect, respectively
r estimate of the count rate ρ
i i
τ , τ relaxation time constant of a ratemeter used for the measurement of the gross effect
g 0
and of the background effect, respectively
α, β probability of a false positive and false negative decision, respectively
1−γ
probability for the coverage interval of the measurand
q quantile of a distribution for the probability p
p
5 Summary of procedures for evaluating and reporting uncertainty and
characteristic limits
This clause gives in a concise form the procedure to be followed for evaluating a measurement of a single
measurand on the basis of the ISO/IEC Guide 98-3:2008/Suppl 1:2008 and calculating the characteristic
limits, i.e. the decision threshold, the detection limit and the limits of a coverage interval. This procedure is
universally suitable, also in cases when the ISO/IEC Guide 98-3 approximation cannot be used or if the latter
method does not provide a result for the detection limit.

ISO/FDIS 11929-2:2025(en)
It is assumed that the measurand is non-negative. This information is only used when calculating a coverage
interval and the best estimate and its associated uncertainty. It is a further characteristic of measurements
of ionizing radiation that they have to be performed in the presence of a radiation background which has
to be subtracted from a gross measurement quantity. The procedures described in this Standard likewise
are applicable to any measurements where a background or blank contribution has to be subtracted from a
gross quantity.
The procedures stipulated in of the ISO 11929 series and the ISO/IEC Guide 98-3:2008/Suppl 1:2008 are
exclusively based on Bayesian statistics. The probability distribution, fy a , which completely describe
()
Y
the uncertainties are to be derived by the Principle of Maximum Information Entropy (PME) or Bayes
Theorem based on the available information a . The original ISO/IEC Guide 98-3 is contained in the
ISO/IEC Guide 98-3:2008/Suppl 1:2008 as a special case, namely that the available information is
ax={},ux() only. But also in this case the ISO/IEC Guide 98-3:2008/Suppl 1:2008 has not the restriction
regarding linearization of the model and is no longer an approximation.
It is assumed in this document that the user has considered beforehand the applicability of the
ISO/IEC Guide 98-3 and has decided that it is necessary and suitable to proceed according to the
ISO/IEC Guide 98-3:2008/Suppl 1:2008 and ISO 11929-2. See Figure 1 of ISO/FDIS 11929-1 for guidance.
The application of this document is structured into 8 consecutive steps. A detailed workflow of this
document is given in Figure 1. Guidance for practically applying Monte Carlo methods is gi
...