ISO 11843-7:2018
(Main)Capability of detection — Part 7: Methodology based on stochastic properties of instrumental noise
Capability of detection — Part 7: Methodology based on stochastic properties of instrumental noise
Background noise exists ubiquitously in analytical instruments, whether or not a sample is applied to the instrument. This document is concerned with mathematical methodologies for estimating the minimum detectable value in case that the most predominant source of measurement uncertainty is background noise. The minimum detectable value can directly and mathematically be derived from the stochastic characteristics of the background noise. This document specifies basic methods to — extract the stochastic properties of the background noise, — use the stochastic properties to estimate the standard deviation (SD) or coefficient of variation (CV) of the response variable, and — calculate the minimum detectable value based on the SD or CV obtained above. The methods described in this document are useful for checking the detection of a certain substance by various types of measurement equipment in which the background noise of the instrumental output predominates over the other sources of measurement uncertainty. Feasible choices are visible and ultraviolet absorption spectrometry, atomic absorption spectrometry, atomic fluorescence spectrometry, luminescence spectrometry, liquid chromatography and gas chromatography.
Capacité de détection — Partie 7: Méthodologie basée sur les propriétés stochastiques du bruit instrumental
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 11843-7
Second edition
2018-09
Capability of detection —
Part 7:
Methodology based on stochastic
properties of instrumental noise
Capacité de détection —
Partie 7: Méthodologie basée sur les propriétés stochastiques du bruit
instrumental
Reference number
©
ISO 2018
© ISO 2018
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ii © ISO 2018 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Quantitative analysis and background noise . 3
4.1 Error sources of analysis . 3
4.2 Random processes in background . 3
5 Theories for precision . 4
5.1 Theory based on auto-covariance function . 4
5.2 Theory based on power spectrum . 6
6 Practical use of FUMI theory . 9
6.1 Estimation of noise parameters by Fourier transform . 9
6.2 Estimation of noise parameters by autocovariance function .11
6.3 Procedures for estimation of SD .11
Annex A (informative) Symbols and abbreviated terms used in this document.14
Annex B (informative) Derivation of Formula (7) .15
Annex C (informative) Derivation of Formulae (14) to (16) .16
Bibliography .18
Foreword
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.org/iso/foreword .html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 6, Measurement methods and results.
This second edition cancels and replaces the first edition (ISO 11843-7:2012), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— created a new 6.2;
— 6.2 of the first edition is renumbered 6.3.
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 2018 – All rights reserved
Introduction
The series of ISO 11843 is based on the probability distributions of the net state variable (measurand)
for both the linear and nonlinear calibration situations. The focus is implicitly, though sometimes
explicitly, on the uncertainty associated with an estimate of the measured response predominantly
coming from the baseline noise in instrumental analysis. In many, if not most, analytical instruments,
the baseline noise is considered the prime cause of uncertainty when the sample amount is as low as the
minimum detectable value. Within its domain of applicability, the method given in this document can
dispense with the repetition of real samples, thus helping to improve global environments by saving
time and energy that would be required by repetition.
The basic concept of ISO 11843-7 is the mathematical description of the probability distribution of
the response variable in terms of mathematically well-defined random processes. This description
straightforwardly leads to the minimum detectable value. As for the relation of the response and
measurand, linear and nonlinear calibration functions can be applied. In this manner, compatibility
with ISO 11843-2 and ISO 11843-5 is ensured.
The definition and applicability of the minimum detectable value are described in ISO 11843-1 and
ISO 11843-2; the definition and applicability of the precision profile are described in ISO 11843-5. The
precision profile expresses how the precision changes depending on the net state variable. ISO 11843-7
specifies the practical use of the fundamental concepts in ISO 11843 in case of the background noise
predominance in instrumental analysis.
The minimum detectable value, x , is generally expressed in the unit of the net state variable. If the
d
calibration function is linear, the SD or CV of the response variable estimated in this document can
linearly be transformed to the SD or CV of the net state variable, which in turn can be used for the
estimation of the minimum detectable value, x .
d
If the calibration function is nonlinear, the precision profile of the response variable in this document
needs to be transformed to the precision profile of the net state variable as shown in ISO 11843-5. In
this situation, the contents of ISO 11843-5 can be used for this purpose without modification.
INTERNATIONAL STANDARD ISO 11843-7:2018(E)
Capability of detection —
Part 7:
Methodology based on stochastic properties of
instrumental noise
1 Scope
Background noise exists ubiquitously in analytical instruments, whether or not a sample is applied
to the instrument. This document is concerned with mathematical methodologies for estimating the
minimum detectable value in case that the most predominant source of measurement uncertainty is
background noise. The minimum detectable value can directly and mathematically be derived from the
stochastic characteristics of the background noise.
This document specifies basic methods to
— extract the stochastic properties of the background noise,
— use the stochastic properties to estimate the standard deviation (SD) or coefficient of variation (CV)
of the response variable, and
— calculate the minimum detectable value based on the SD or CV obtained above.
The methods described in this document are useful for checking the detection of a certain substance
by various types of measurement equipment in which the background noise of the instrumental
output predominates over the other sources of measurement uncertainty. Feasible choices are visible
and ultraviolet absorption spectrometry, atomic absorption spectrometry, atomic fluorescence
spectrometry, luminescence spectrometry, liquid chromatography and gas chromatography.
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 3534-2, Statistics — Vocabulary and symbols — Part 2: Applied statistics
ISO 3534-3, Statistics — Vocabulary and symbols — Part 3: Design of experiments
ISO 5725-1, Accuracy (trueness and precision) of measurement methods and results — Part 1: General
principles and definitions
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 11843-5, Capability of detection — Part 5: Methodology in the linear and non-linear calibration cases
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 3534-1, ISO 3534-2,
ISO 3534-3, ISO 5725-1, ISO 11843-1, ISO 11843-2, ISO 11843-5 and the following apply. A list of symbols
and abbreviated terms used in this document is provided in Annex A.
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/
3.1
precision profile
mathematical description of the standard deviation (SD) of the response variable
[σ (X)] or net state variable [σ (X)] as a function of the net state variable
Y X
Note 1 to entry: The coefficient of variation (CV) of the response variable or net state variable as a function of the
net state variable is also referred to as a precision profile.
Note 2 to entry: Precision means the SD or CV of the observed response variable or SD or CV of the net state
variable when estimated by the calibration function (see ISO 11843-5).
[SOURCE: ISO 11843-5:2008, 3.4, modified — “coefficient of variation” has been removed and Note 1 to
entry has been added instead. Note 2 to entry has also been added.]
3.2
minimum detectable value of the net state variable
x
d
value of the net state variable in the actual state that will lead, with probability 1 – β, to the conclusion
that the system is not in the basic state
Note 1 to entry: Under the assumption that the SD, σ (X), of the net state variable is constant [(σ (X) = σ ], the
X X X
minimum detectable value, x , is defined as
d
xk=+ k σ (1)
()
dc d X
where
k denotes a coefficient to specify the probability of an error of the first kind;
c
k is a coefficient to specify the probability of an error of the second kind.
d
If the SD, σ , of the response variable is assumed to be constant [σ (X) = σ ], then the minimum detectable value
Y Y Y
can be calculated by the following Formula (2):
xk=+ k σ //ddYX (2)
()()
dc d Y
where |dY/dX| denotes the absolute value of the slope of the linear calibration function and is constant.
Note 2 to entry: If the net state variable is normally distributed, the coefficients k = k = 1,65 specify the
c d
probabilities of an error of the first and second kinds (= 5 %) and Formula (1) can simply be written as x = 3,30σ .
d X
Note 3 to entry: If k = k = 1,65, Formula (1) takes the form that σ / x = 1/3,30 = 30 %. Therefore, x can be
c d
...
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