ISO 11843-6:2025

International
Standard
ISO 11843-6
Third edition
Capability of detection —
2025-10
Part 6:
Methodology for the determination
of the critical value and the
minimum detectable value in
Poisson distributed measurements
by normal approximations
Capacité de détection —
Partie 6: Méthodologie pour la détermination de la valeur
critique et de la valeur minimale détectable pour les mesures
distribuées selon la loi de Poisson approximée par la loi Normale
Reference number
© ISO 2025
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
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Measurement system and data handling . 2
6 Computation by approximation . 3
6.1 The critical value based on the normal distribution .3
6.2 Determination of the critical value of the response variable .4
6.3 Sufficient capability of the detection criterion .5
6.4 Confirmation of the sufficient capability of detection criterion .6
7 Reporting the results from an assessment of the capability of detection . 7
8 Reporting the results from an application of the method . 7
Annex A (informative) Estimating the mean value and variance when the Poisson distribution
is approximated by the normal distribution . 8
Annex B (informative) Accuracy of approximations . 9
Annex C (informative) Selecting the number of channels for the detector .15
Annex D (informative) Examples of calculations .16
Bibliography .21

iii
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 document 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 Technical Committee ISO/TC 69, Application of statistical methods,
Subcommittee SC 6, Measurement methods and results.
This third edition cancels and replaces the second edition (ISO 11843-6:2019), which has been technically
revised.
The main changes are as follows:
— the symbols were modified to conform to ISO 11843-1;
— a list of symbols was moved from Annex A to Clause 4;
— in 6.3, explanatory text of how to determine the minimum detectable value was added;
— Clause 8 was revised to provide a description of the appropriate approach for determining whether or
not the target substance has been detected;
— typographic and obvious errors were corrected.
A list of all parts in the ISO 11843 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
Introduction
Many types of instruments use the pulse-counting method for detecting signals. X-ray, electron and ion-
spectroscopy detectors, such as X-ray diffractometers (XRD), X-ray fluorescence spectrometers (XRF), X-ray
photoelectron spectrometers (XPS), Auger electron spectrometers (AES), secondary ion mass spectrometers
(SIMS) and gas chromatograph mass spectrometers (GCMS) are of this type. These signals consist of a series
of pulses produced at random and irregular intervals. They can be understood statistically using a Poisson
distribution and the methodology for determining the minimum detectable value can be deduced from
statistical principles.
Determining the minimum detectable value of signals is sometimes important in practical work. The
value provides a criterion for deciding when “the signal is certainly not detected”, or when “the signal is
[1]to[8]
significantly different from the background noise level” . For example, it is valuable when measuring the
presence of hazardous substances or surface contamination of semi-conductor materials. RoHS (Restrictions
on Hazardous Substances) sets limits on the use of six hazardous materials (hexavalent chromium, lead,
mercury, cadmium and the flame retardant agents, perbromobiphenyl, PBB, and perbromodiphenyl ether,
PBDE) in the manufacturing of electronic components and related goods sold in the EU. For that application,
XRF and GCMS are the testing instruments used. XRD is used to measure the level of hazardous asbestos
and crystalline silica present in the environment or in building materials.
Although the methodology employed to determine the minimum detection values has long been established
in the field of chemical analysis, it has hitherto remained undefined within the domain of pulse count
measurements. The necessity of establishing a methodology for determining the minimum detectable value
[9]
in this field is duly acknowledged .
In this document the Poisson distribution is approximated by the normal distribution, ensuring consistency
with the IUPAC approach laid out in the ISO 11843 series. The conventional approximation is used to generate
the variance, the critical value of the response variable, the capability of detection criteria and the minimum
[10]
detectability level .
In this document:
— α is the probability of erroneously detecting that a system is not in the basic state, when really it is in
that state;
— β is the probability of erroneously not detecting that a system is not in the basic state when the value of
the state variable is equal to the minimum detectable value(x ).
D
v
International Standard ISO 11843-6:2025(en)
Capability of detection —
Part 6:
Methodology for the determination of the critical value
and the minimum detectable value in Poisson distributed
measurements by normal approximations
1 Scope
This document presents methods for determining the critical value of the response variable and the
minimum detectable value in Poisson distribution measurements. It is applicable when variations in
both the background noise and the signal are describable by the Poisson distribution. The conventional
approximation is used to approximate the Poisson distribution by the normal distribution consistent with
ISO 11843-3 and ISO 11843-4.
The accuracy of the normal approximation as compared to the exact Poisson distribution is discussed in
Annex B.
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 Guide 30, Reference materials — Selected terms and definitions
ISO 3534-1, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in
probability
ISO 11843-1, Capability of detection — Part 1: Terms and definitions
ISO 11843-2, Capability of detection — Part 2: Methodology in the linear calibration case
ISO 11843-3, Capability of detection — Part 3: Methodology for determination of the critical value for the
response variable when no calibration data are used
ISO 11843-4, Capability of detection — Part 4: Methodology for comparing the minimum detectable value with
a given value
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 11843-1, ISO 11843-2,
ISO 11843-3, ISO 11843-4, and ISO Guide 30 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/

4 Symbols
X
state variable
Y
response variable
number of replications of measurements on the reference material representing the value of the basic
J
state variable (blank sample)
K
number of replications of measurements on the actual state (test sample)
number of replications of measurements of each reference material in assessment of the capability
N
of detection
x
a value of state variable
y
a value of response variable
y
critical value of the response variable defined by ISO 11843-1 and ISO 11843-3
C
x
given value which is tested to determine whether it is greater than the minimum detectable value
g
x
minimum detectable value of the state variable
D
σ
standard deviation under actual performance conditions for the response in the basic state
b
σ
standard deviation under actual performance conditions for the response in a sample with the state
g
variable equal to x
g
η
expected value under the actual performance conditions for the response in the basic state
b
η
expected value under the actual performance conditions for the response in a sample with the state
g
variable equal to x
g
y
the arithmetic mean of the actual measured response in the basic state
b
y the arithmetic mean of the actual measured response in a sample with the state variable equal to x
g g
y minimum detectable response value with the state variable equal to x
D d
λ
mean value corresponding to the expected number of events in Poisson distribution
α
the probability that an error of the first kind has occurred
β
the probability that an e
...