prEN ISO 11929-2

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:

Determination of the characteristics limits (decision threshold, detection limit and limits of

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)

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 2

3 Terms and definitions ..................................................................................................................................................................................... 2

4 Quantities and symbols ................................................................................................................................................................................. 6

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

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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

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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

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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.

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

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

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

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

— the “decision threshold” allows a decision to be made on whether or not the physical effect quantified

— 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

— 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

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

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

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 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

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

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

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

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

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

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

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

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

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

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 ,

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

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

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

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

ISO/IEC Guide 98-3, Uncertainty of measurement — Part 1: Guide to the expression of uncertainty in

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

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

process of experimentally obtaining one or more quantity values that can reasonably be attributed to a

interval containing the set of true quantity values of a measurand with a stated probability, based on

Note 1 to entry: A coverage interval does not need to be centred on the chosen measured quantity value (see

Note 2 to entry: A coverage interval should not be termed “confidence interval” to avoid confusion with the

generic description of a logical organization of operations used in a measurement

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

set of quantity values being attributed to a measurand together with any other available relevant

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

non-negative parameter characterizing the dispersion of the quantity values being attributed to a

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,

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

set of mathematical relationships between all measured and other quantities involved in the evaluation

Note 1 to entry: The model of evaluation does not need to be an explicit function; it can also be an algorithm

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

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

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.

smallest true value of the measurand which ensures a specified probability of being detectable by the

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

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