ISO 11843-6:2019

INTERNATIONAL ISO
STANDARD 11843-6
Second edition
2019-02
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
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 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Measurement system and data handling . 2
5 Computation by approximation. 2
5.1 The critical value based on the normal distribution . 2
5.2 Determination of the critical value of the response variable . 4
5.3 Sufficient capability of the detection criterion . 5
5.4 Confirmation of the sufficient capability of detection criterion . 5
6 Reporting the results from an assessment of the capability of detection .6
7 Reporting the results from an application of the method . 7
Annex A (informative) Symbols used in this document . 8
Annex B (informative) Estimating the mean value and variance when the Poisson
distribution is approximated by the normal distribution .10
Annex C (informative) An accuracy of approximations .11
Annex D (informative) Selecting the number of channels for the detector .17
Annex E (informative) Examples of calculations .18
Bibliography .23
Foreword
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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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
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.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 second edition cancels and replaces the first edition (ISO 11843-6:2013, corrected version issued
in 2014), of which it constitutes a minor revision. The changes compared to the previous corrected
version are as follows:
— the following updates have been made to add clarity or to correct typographic and obvious errors:
— in Formula (2) and the related Note, “±” is replaced with “+”;
nd
— in 5.4, 2 paragraph, “100(1-α/2)%” is replaced with “100(1-α)%”, and “described below by the
general theory of estimation” is inserted at the end,
rd
— in Clause 6 e), Figure 1, and Annex C 3 paragraph, the average values ( y , y and y ) are used;
b d g
rd st
— in Annex C, 3 paragraph, 1 sentence, “independent” is inserted before “variables”;
— in the line below Formula (C.1), I • is consistently replaced with I • ;
() ()
k y
nd
— in E.2, 2 paragraph, the text has been slightly reworded for clarity;
— thorough the text, minor editorial modifications have been made in line with the 2018 edition of the
ISO/IEC Directives, Part 2.
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 © ISO 2019 – All rights reserved

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]-[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.
The methods used to set the minimum detectable value have for some time been in widespread use
in the field of chemical analysis, although not where pulse-counting measurements are concerned.
The need to establish a methodology for determining the minimum detectable value in that area is
[9]
recognized .
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
[10]
criteria and the minimum 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
This document is fully compliant with ISO 11843-1, ISO 11843-3 and ISO 11843-4.
INTERNATIONAL STANDARD ISO 11843-6:2019(E)
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 C.
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 terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
4 Measurement system and data handling
The conditions under which Poisson counts are made are usually specified by the experimental set-up.
The number of pulses that are detected increases with both the time and with the width of the region
over which the spectrum is observed. These two parameters should be noted and not changed during
the course of the measurement.
The following restrictions should be observed if the minimum detectable value is to be determined
reliably:
a) Both the signal and the background noise should follow the Poisson distributions. The signal is the
mean value of the gross count.
b) The raw data should not receive any processing or treatment, such as smoothing.
c) Time interval: Measurement over a long period of time is preferable to several shorter
measurements. A single measurement taken for over one second is better than 10 measurements
over 100 ms each. The approximation of the Poisson distribution by the normal distribution is more
reliable with higher mean values.
d) The number of measurements: Since only mean values are used in the approximations presented
here, repeated measurements are needed to determine them. The power of test increases with the
number of measurements.
e) Number of channels used by the detector: There should be no overlap of neighbouring peaks. The
number of channels that are used to measure the background noise and the sample spectra should
be identical (Annex D, Figure D.1).
f) Peak width: The full width at half maximum (FWHM) is the recom
...