SIST EN ISO 11929-2:2021

SLOVENSKI STANDARD
oSIST prEN ISO 11929-2:2020
01-december-2020
Ugotavljanje karakterističnih mej (odločitveni prag, zaznavanje meje in omejitev
intervala pokritja) pri meritvah ionizirnega sevanja - Osnove in uporaba - 2. del:
Napredne aplikacije (ISO 11929-2:2019)
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)
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 11929-2:2019)
Ta slovenski standard je istoveten z: prEN ISO 11929-2
ICS:
17.240 Merjenje sevanja Radiation measurements
oSIST prEN ISO 11929-2:2020 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
oSIST prEN ISO 11929-2:2020

---------------------- Page: 2 ----------------------
oSIST prEN ISO 11929-2:2020
INTERNATIONAL ISO
STANDARD 11929-2
Second edition
2019-02
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
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
Reference number
ISO 11929-2:2019(E)
©
ISO 2019

---------------------- Page: 3 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

---------------------- Page: 4 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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 . 9
6 Evaluation of a measurement on the basis of ISO/IEC Guide 98-3-1 .12
6.1 Introduction and decisions to be made .12
6.2 General aspects concerning the measurand and the model of evaluation .12
6.3 Establishing probability distributions for the input quantities .13
6.4 Propagating probability distributions .15
6.5 Evaluation of the primary measurement result .16
6.6 Standard uncertainty associated with the primary measurement result .16
7 PDF for an assumed true value of the measurand .17
8 Decision threshold, detection limit and assessments .17
8.1 Specifications.17
8.2 Decision threshold .17
8.3 Detection limit .18
8.4 Assessments .19
9 Limits of the coverage interval .19
9.1 General Aspects .19
9.2 The probabilistically symmetric coverage interval .20
9.3 The shortest coverage interval .20
10 The best estimate and its associated standard uncertainty .21
11 Documentation .21
Annex A (normative) Measurements with low count numbers .23
Annex B (informative) Explanatory notes .25
Bibliography .39
© ISO 2019 – All rights reserved iii

---------------------- Page: 5 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/patents).
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 This document was prepared by ISO/TC 85, Nuclear energy, nuclear
technologies, and radiological protection, Subcommittee SC 2, Radiological protection.
This second edition of ISO 11929-2 together with ISO 11929-1, ISO 11929-3, cancels and replaces
ISO 11929:2010 which have been technically revised, specifically with reference to the type of statistical
treatment of the data and extended with respect to the methodology of uncertainty assessment from
the ISO/IEC Guide 98-3:2009, to the ISO/IEC Guide 98-3-1:2008.
A list of all the parts in the ISO 11929 series can be found on the ISO website.
iv © ISO 2019 – All rights reserved

---------------------- Page: 6 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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 98-3-1 and ISO/IEC 98-3-2.
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 98-3-1; 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 makes
[14 to 16]
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
[9] [10] [11]
characteristic 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.
© ISO 2019 – All rights reserved v

---------------------- Page: 7 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

Since the ISO/IEC Guide 98-3-1 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
Bayesian statistics and can serve as a bridge between ISO 11929:2010 and the ISO/IEC Guide 98-3-
1. 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. 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 98-3-2 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 98-3-1. 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 © ISO 2019 – All rights reserved

---------------------- Page: 8 ----------------------
oSIST prEN ISO 11929-2:2020
INTERNATIONAL STANDARD ISO 11929-2:2019(E)
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 Annex A of ISO 11929-1:2019 the special case of
repeated counting measurements with random influences is covered, while measurements with linear
analogous ratemeters are covered in Annex B of ISO 11929-1:2019.
This document extends the former ISO 11929:2010 to the evaluation of measurement uncertainties
according to the ISO/IEC Guide 98-3-1. It also presents some explanatory notes regarding general
aspects of counting measurements and on Bayesian statistics in measurements.
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
[30,31]
and on its current development may be found elsewhere .
© ISO 2019 – All rights reserved 1

---------------------- Page: 9 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

ISO 11929 also applies analogously to other measurements of any kind especially if a similar model
[1]
of the evaluation is involved. Further practical examples can be found, for example, in ISO 18589 ,
[2] [3] [4] [5] [6] [7] [8]
ISO 9696 , ISO 9697 , ISO 9698 , ISO 10703 , ISO 7503 , ISO 28218 , and ISO 11885 .
NOTE A code system, named UncertRadio, is available for calculations according to ISO 119291 to
[27][28]
ISO 11929-3. UncertRadio can be downloaded for free from https: //www .thuenen .de/en/fi/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
[32]
language can be 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 part of ISO 11929 in a spreadsheet containing a Monte Carlo add-in or into other
commercial mathematics software.
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 1: Guide to the expression of uncertainty in
measurement, JCGM 100:2008
ISO/IEC Guide 98-3-1, 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 98-3-2, 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), JCGM 200:2012
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 98-3-1, ISO/IEC 98-3-2, 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 http: //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]
2 © ISO 2019 – All rights reserved

---------------------- Page: 10 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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]
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, 2.4]
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]
© ISO 2019 – All rights reserved 3

---------------------- Page: 11 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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.
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.
4 © ISO 2019 – All rights reserved

---------------------- Page: 12 ----------------------
oSIST prEN ISO 11929-2:2020
ISO 11929-2:2019(E)

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: The decision threshold is defined such that in cases where the measurement result, y, exceeds
the decision threshold, y* , the probability that the true value of the measurand is zero is less or equal to a
chosen probability for a wrong decision, α.
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.
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: With the decision threshold according to 4.13, the detection limit is the smallest true value of the
measurand for which the probability of wrongly deciding that the true value of the measurand is zero is equal to
a specified value, β, when, in fact, the true value of the measurand is not zero. The probability of being detectable
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
...