ISO 11352:2025

International
Standard
ISO 11352
Second edition
Water quality — Estimation of
2025-09
measurement uncertainty based on
validation and quality control data
Qualité de l'eau — Estimation de l'incertitude de mesure basée
sur des données de validation et de contrôle qualité
Reference number
© ISO 2025
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 4
5 Principle . 5
6 Procedure . 6
7 Preparative considerations for the estimation of measurement uncertainty . 6
7.1 Specification of the measurement .6
7.2 Specification of the parametric form in which the measurement uncertainty is reported .7
8 Evaluation of available data for within-laboratory reproducibility and bias . 7
8.1 Approach and criteria .7
8.2 Within-laboratory reproducibility .8
8.2.1 General .8
8.2.2 Quality control samples covering the whole analytical process .9
8.2.3 Using standard solutions and replicates of test samples .9
8.2.4 No stable quality control samples .10
8.3 Bias .10
8.3.1 General .10
8.3.2 Analysis of suitable reference materials .11
8.3.3 Participation in interlaboratory comparisons . 12
8.3.4 Recovery experiments. 13
9 Calculation of the combined standard uncertainty .15
10 Calculation of the expanded uncertainty .16
11 Initial estimation of measurement uncertainty from reproducibility standard deviation .16
12 Report .16
Annex A (informative) Division of the measurement range into two parts — Constant absolute
and constant relative uncertainties . 17
Annex B (normative) Estimation of the pooled standard deviation from replicate measurements .24
Annex C (informative) Examples of the estimation of measurement uncertainty .25
Bibliography .38

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
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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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
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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 147, Water quality, Subcommittee SC 2,
Physical, chemical and biochemical methods.
This second edition cancels and replaces the first edition (ISO 11352:2012), which has been technically
revised.
The main changes are as follows:
— requirements for measurements for estimation of uncertainty component for the within-laboratory
reproducibility have been changed from at least eight to 20 replicates with exception of a first estimation;
— the use of data from target control charts estimation of precision has been described;
— a new informative annex has been introduced to describe how to divide the measurement range into two
parts for constant absolute and constant relative uncertainties;
— in Annex B (former Annex A) the estimation of the standard uncertainty from range control charts has
been changed to the use of pooled standard deviation;
— the examples in Annex C have been adjusted;
— this document has been editorially revised.
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
[1]
The basic principles of the estimation of measurement uncertainty are set out in ISO/IEC Guide 98-3.
There are several ways of estimating measurement uncertainty depending on the purpose of the estimation
[2]
and the available data; Eurolab TR 1/2007 gives an overview of the main approaches.
This document specifies a set of procedures to enable laboratories to estimate the measurement uncertainty
of their results, using an approach based on validation and quality control data. Validation data can be used
for first estimates of the measurement uncertainty, but should later be confirmed with data from quality
control, when the method is in routine use. It is structured in a way that is applicable to analysts that do not
have a thorough understanding of metrology or statistics.
[3]
Nordtest TR 537 has been used as a basis for developing this document. The approach taken is “top-down”,
[1]
contrary to the mainly “bottom-up” strategy adopted in ISO/IEC Guide 98-3 .
It is statistically acceptable to combine the uncertainty components associate with within-laboratory
reproducibility for random error and the uncertainty associated the bias for systematic error into a single
measure of uncertainty. The sources of data for this approach are validation and analytical quality control.
The experimental approach specified in this document enables a good coverage of the sources of variation
observed during routine use of the analytical method.

v
International Standard ISO 11352:2025(en)
Water quality — Estimation of measurement uncertainty
based on validation and quality control data
1 Scope
This document specifies approaches for the estimation of measurement uncertainty of chemical and
physicochemical methods in single laboratories based on validation data and quality control data obtained
within the field of water analysis. However, this approach can also be used in many other areas of chemical
analysis.
NOTE 1 The principles of the estimation of uncertainty specified in this document are consistent with the principles
described in ISO/IEC Guide 98-3.
In this document, the quantification of measurement uncertainty relies on performance characteristics of a
measurement procedure obtained from validation and the results of internal and external quality control.
[3] [4]
NOTE 2 The approaches specified in this document are mainly based on Nordtest TR 537 , but also QUAM , and
[2]
Eurolab TR 1/2007 .
NOTE 3 This document only addresses the evaluation of measurement uncertainty for results obtained from
quantitative measurement procedures. The uncertainties associated with results obtained from qualitative
procedures are not considered.
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/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated
terms (VIM)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99 and the following 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/
3.1
precision
measurement precision
closeness of agreement between indications or measured quantity values obtained by replicate
measurements on the same or similar objects under specified conditions
[SOURCE: ISO/IEC Guide 99:2007 2.15, modified — Notes 1 to 4 to entry have been deleted.]

3.2
error
measurement error
measured quantity value minus a reference quantity value
[SOURCE: ISO/IEC Guide 99:2007, 2.16, modified — the admitted term "error of measurement" and Notes 1
and 2 to entry have been deleted.]
3.3
systematic error
systematic measurement error
component of measurement error (3.2) that in replicate measurements remains constant or varies in a
predictable manner
[SOURCE: ISO/IEC Guide 99:2007, 2.17, modified — the admitted term "systematic error of measurement"
and Notes 1 to 3 to entry have been deleted.]
3.4
bias
measurement bias
estimate of a systematic measurement error (3.3)
[SOURCE: ISO/IEC Guide 99:2007, 2.18]
3.5
random error
random measurement error
component of measurement error (3.2) that in replicate measurements varies in an unpredictable manner
[SOURCE: ISO/IEC Guide 99:2007, 2.19, modified — Notes 1 to 3 to entry have been deleted.]
3.6
repeatability condition
condition of measurement, out of a set of conditions that includes the same measurement procedure,
same operators, same measuring system, same operating conditions and same location, and replicate
measurements on the same or similar objects over a short period of time
[SOURCE: ISO/IEC Guide 99:2007, 2.20, modified — the term "repeatability condition of measurement" and
Notes 1 and 2 to entry have been deleted.]
3.7
repeatability
measurement precision (3.1) under a set of repeatability conditions (3.6) of measurement
[SOURCE: ISO/IEC Guide 99:2007, 2.21, modified — the term "measurement repeatability" has been deleted.]
3.8
analytical run
series of measurements made under repeatability conditions (3.6)
3.9
within-laboratory reproducibility
intermediate measurement precision (3.1)where all variations that occur within one laboratory are included
Note 1 to entry: Intermediate measurement precision is defined in ISO/IEC Guide 99: 2007, 2.23.

3.10
reproducibility condition
condition of measurement, out of a set of conditions that includes different locations, operators, measuring
systems, and replicate measurements on the same or similar objects
[SOURCE: ISO/IEC Guide 99:2007, 2.24, modified — the term "reproducibility condition of measurement"
Notes 1 and 2 to entry have been deleted.]
3.11
reproducibility
measurement precision (3.1) under reproducibility conditions (3.10) of measurement
[SOURCE: ISO/IEC Guide 99:2007, 2.25, modified — the term "measurement reproducibility" and Note 1 to
entry have been deleted.]
3.12
uncertainty
measurement uncertainty
non-negative parameter characterizing the dispersion of the quantity values being attributed to a
measurand, based on the information used
[SOURCE: ISO/IEC Guide 99:2007, 2.26, modified — Notes 1 to 4 to entry have been deleted.]
3.13
standard uncertainty
standard measurement uncertainty
measurement uncertainty (3.12) expressed as a standard deviation
[SOURCE: ISO/IEC Guide 99:2007, 2.30, modified — the admitted term "standard uncertainty of
measurement" has been deleted.]
3.14
combined standard uncertainty
combined standard measurement uncertainty
standard measurement uncertainty (3.13) that is obtained using the individual standard measurement
uncertainties associated with the input quantities in a measurement model
[SOURCE: ISO/IEC Guide 99:2007, 2.31, modified — Note 1 to entry has been deleted.]
3.15
target measurement uncertainty
target uncertainty
measurement uncertainty (3.12) specified as an upper limit and decided on the basis of the intended use of
measurement results
[SOURCE: ISO/IEC Guide 99:2007, 2.34]
3.16
expanded uncertainty
expanded measurement uncertainty
product of a combined standard measurement uncertainty (3.14) and a factor larger than the number one
Note 1 to entry: The term “factor” in this definition refers to a coverage factor (3.17).
[SOURCE: ISO/IEC Guide 99:2007, 2.35, modified — Notes 1 and 3 to entry have been deleted.]
3.17
coverage factor
number larger than one by which a combined standard measurement uncertainty (3.14) is multiplied to obtain
an expanded measurement uncertainty (3.16)
[SOURCE: ISO/IEC Guide 99:2007, 2.38, modified — Note 1 to entry has been deleted.]

3.18
quality control sample
reference material used for quality control
[6]
Note 1 to entry: For more information on reference materials, see ISO Guide 30.
Note 2 to entry: Quality control samples may or may not have a reference value.
4 Symbols
b bias estimated as the difference between mean measured value and an accepted reference value
th
b i bias of a series of biases estimated as the difference between mean measured value and an
i
accepted reference value
b root mean square (quadratic mean) of the b values
rms i
c concentration
c transition point between absolute and relative uncertainties
T
th
D difference between the measurement result and the assigned value of the i sample of the inter-
i
laboratory comparison
D root mean square (quadratic mean) of the differences
rms
i variable related to an observation of a series
j variable related to a source of uncertainty
J total number of sources of uncertainty
k coverage factor
n number of analysed interlaboratory comparison samples
ilc
n number of measurements
M
n number of participating laboratories for sample i
p,i
n number of reference materials
r
n number of recovery experiments
η
s standard deviation
s standard deviation of the measured values of the reference material
b
s pooled standard deviation
p
s reproducibility standard deviation from the interlaboratory comparison for sample i
R,i
s
within-laboratory reproducibility standard deviation
R
w
s
relative within-laboratory reproducibility standard deviation
R ,rel
w
U expanded uncertainty
U relative expanded uncertainty
rel
u combined standard uncertainty
c
u combined relative standard uncertainty
c,rel
u standard uncertainties from different sources j
j
u relative standard uncertainties from different sources j
j,rel
u standard uncertainty in the concentration of the analyte added
add
u standard uncertainty component associated with bias
b
u standard uncertainty of the concentration of the addition solution
conc
u
mean standard uncertainty of the reference values or mean standard uncertainty of the assigned
C
ref
values of the interlaboratory comparison samples
u
standard uncertainty of the reference value
C
ref
u
standard uncertainty of the assigned value of the interlaboratory sample i
Ci,
ref
u
standard uncertainty component for the within-laboratory reproducibility
R
w
u
relative standard uncertainty component for the within-laboratory reproducibility
R,rel
w
u standard uncertainty component from the range control chart (obtained under repeatability
r,range
conditions)
u
standard uncertainty component resulting from variations between analytical runs
R,run
w
u
standard uncertainty component of the results from the standard solution which is used as a
Rs, tand
w
quality control sample
u standard uncertainty component of the volume added
V
u systematic standard uncertainty component of the volume added
V,b
u random standard uncertainty component of the volume added (obtained under repeatability
V,rep
conditions)
ε maximum deviation of the volume from the specified value (producer information)
V,max
η
recovery
5 Principle
A measurement result of a laboratory is an estimate of the value of the measurand. The quality of this
estimate depends on the inevitable uncertainty that is inherent to the measurement result. In principle, the
measurement uncertainty is a property of individual measurement results.
This document specifies procedures for the estimation of measurement uncertainty within the scope of the
analytical method. The estimation of the measurement uncertainty for each individual measurement result
is usually not necessary, if the laboratory can demonstrate that the identified critical influencing factors
[7]
are under control. The estimation of the measurement uncertainty applies to measurement results,
independently of, for example, sample matrix variations or different analysts. The uncertainty estimation
needs to consider both random and systematic errors.
The estimation of measurement uncertainty is based on validation and quality control data which represent
the within-laboratory reproducibility and the bias.

6 Procedure
The procedure for the estimation of measurement uncertainty consists of the steps shown schematically in
Figure 1. It gives references to appropriate clauses and subclauses within this document.
Figure 1 — Schematic procedure for the estimation of measurement uncertainty
In general, within-laboratory reproducibility (random error) and the bias (systematic error) are determined
independently using suitable data from validation and quality control data.
The combined standard uncertainty, i.e. the root of the quadratic sum of the standard uncertainty component
for the within-laboratory reproducibility and the standard uncertainty component associated with bias, is
multiplied by a factor of two to obtain the expanded uncertainty at a confidence level of approximately 95 %.
If the measurement uncertainty varies significantly, depending on either the matrix or the concentration
range, or both, the uncertainty estimation shall be made separately for either each matrix or each
concentration range, or both.
NOTE The generic term ‘concentration’ is used on its own, i.e. unqualified, when a generality is required. It represents
the family of terms which includes, mass fraction, mass concentration, amount of substance concentration etc.
7 Preparative considerations for the estimation of measurement uncertainty
7.1 Specification of the measurement
Before starting the estimation of measurement uncertainty, it is necessary that the analyst specifies the
analytical method under consideration, and the objectives and purposes of the measurement. The following
list is a minimal checklist for this specification.

The specification comprises:
— the measurand;
— the measurement procedure;
— the field of application (matrices, concentration range).
7.2 Specification of the parametric form in which the measurement uncertainty is reported
The expanded uncertainty, U, is reported either as an absolute uncertainty value or as a relative uncertainty
value. For results near the limit of quantification, the uncertainty is often found to be constant and can therefore
be expressed as an absolute value. When results are well above the limit of quantification, the uncertainty is
often proportional to the analyte concentration and can therefore be expressed as a relative value.
EXAMPLE Determination of a heavy metal (limit of quantification: 5 µg/l)
— for concentration range 5 µg/l to 20 µg/l: U = 1 µg/l
— for concentration > 20 µg/l: U = 5 %
rel
More information including different approaches to estimate the transition point between absolute and
relative uncertainties is given in Annex A.
Usually, the measurement uncertainty is determined for a certain matrix and concentration range. In some
situations, an interpolation function can be applied between different concentration ranges (see Clause E.5
in Reference [4]).
8 Evaluation of available data for within-laboratory reproducibility and bias
8.1 Approach and criteria
In this document, the uncertainty component for the within-laboratory reproducibility, u , and the
R
w
uncertainty component from bias, u , form the basis for the estimation of the measurement uncertainty. The
b
uncertainty can be estimated in absolute or relative units (%). It is necessary that the measurements are
made not under repeatability conditions, but under “within-laboratory reproducibility conditions” (i.e. on
different days and, depending on the conditions in the respective laboratory, with different equipment,
different calibration and different operators).
Selected validation data and analytical quality control results should represent the measurement
specifications outlined in Clause 7. This involves considerations include, but not limited to:
— all steps of the analysis (including pretreatment and ensuring comparability of the reference materials
to test samples);
— all conditions involved in executing the measurement procedure (e.g. different operators using different
equipment);
— all potential variations in matrices (e.g. drinking water, surface water, sea water, wastewater) and
potential interferences.
Choose, as a basis for the estimation of the uncertainty, the source of experimental information that provides
the best coverage of uncertainty contributions in actual practice. Evaluate whether information exists on
missing uncertainty contributions that are not known to be negligible.
If necessary, complete the uncertainty estimation, based on validation data and quality control results, with
information from additional experiments or with estimations on the basis of existing knowledge.
If overestimation of the measurement uncertainty is acceptable, i.e. if the target measurement uncertainty is
not exceeded, the result of this experimental approach including possible overestimation is still acceptable.

If overestimation is not acceptable, a more detailed estimation shall be performed, which can encompass
part of a modelling approach (for an example, see Reference [4]).
Figure 1 shows a schematic representation of the procedure.
Uncertainty calculations can be performed using either absolute or relative values (see 7.2 and Annex A).
Annex C contains examples of the estimation of measurement uncertainty according to this document.
Measurement uncertainty can be estimated in several ways. Ideally, the estimates should lead to a
statistically identical result. If not, this can be the consequence of not covering all sources of uncertainties.
In this case, the uncertainty is underestimated. It can also occur, however, that even applying the method
correctly leads to an overestimation of the uncertainty. This high value can be the consequence of uncertainty
components not associated with the measurement method under consideration, e.g. those associated with
the reference value of a reference material or the uncertainty of the concentration of a solution used in
recovery experiments.
8.2 Within-laboratory reproducibility
8.2.1 General
The estimation of the random variations of measurement results shall be made under the same conditions
as used during a routine analysis.
These conditions are usually employed when quality control samples are analysed that are similar to test
samples.
For the estimation of the uncertainty component for the within-laboratory reproducibility, u , three
R
w
approaches shown in Figure 1 are described:
— quality control samples covering the whole analytical process in 8.2.2,
— the use of standard solutions and replicates of test samples in 8.2.3, and
— an approach in cases where no stable quality control samples are available in 8.2.4.
It is important to account for long-term variations of certain uncertainty components that can induce
systematic error in the short term within the laboratory. This includes, but is not limited to, the uncertainty
components associated to different stock solutions, new batches of critical reagents and recalibrations of
equipment. A minimum of 20 measurements (though more would be preferable), which should encompass a
diverse range of short-term variation sources, is required for the final estimation of the standard deviation.
For the first estimate of measurement uncertainty (e.g. during the validation of a method), a minimum of
eight measurements is still necessary.
If target control charts with action and warning limits are used, the standard deviation shall be calculated
by dividing the action limit by three for a mean control chart and by 3,69 for a range chart, see Nordtest
[8] [9]
Report TR 569. If acceptance control charts are used as described in ISO 7870-3 with only action limits,
the acceptable range can be seen as a rectangular distribution and the standard deviation shall be calculated
by dividing the action limit by square root of three.
NOTE 1 The target control limits are normally set wider than the control limits which are based on standard
deviation obtained from quality control results.
NOTE 2 A first estimate of the uncertainty can be used when comparing to a target measurement uncertainty
during the validation process.
It is recognized that, while the analysis of at least 20 measurements is appropriate for the vast number of
situations, there are occasions when this is not so. The higher the number of measurements, the higher the
confidence in the estimation. Ideally the used data for the final estimate should cover a time period of e.g.
[8]
one year .
Examples are given in Annex C.
8.2.2 Quality control samples covering the whole analytical process
When quality control samples covering the whole analytical process are available, the standard uncertainty
of the within-laboratory reproducibility, u , can be estimated directly from the standard deviation of
R
w
quality control results (e.g. as obtained from quality control charts). These quality control samples should
meet the following criteria:
— be stable;
— cover the whole analytical process;
— include all sample preparation steps;
— analysed regularly using the conditions described in 8.2.1; and
— similar in matrix and analyte concentration levels to test samples.
In this case, the standard uncertainty of the within-laboratory reproducibility, u , can be derived from
R
w
the standard deviation of the quality control results obtained using these quality control samples according
to Formula (1).
us= (1)
RR
ww
NOTE The quality control samples can be real or spiked samples.
If the analytical method covers a broad concentration range or range of matrices, and the uncertainty
component for the within-laboratory reproducibility, u , varies with the concentration or matrices, it is
R
w
necessary to analyse quality control samples comprising different matrices and concentration levels.
8.2.3 Using standard solutions and replicates of test samples
If quality control samples with a similar matrix to the test samples are not available and synthetic standard
solutions (with a matrix which differs from that of test samples) are used without sample preparation,
the additional uncertainty component due to variations in the sample preparation, possibly increased
inhomogeneity of the analyte in the matrix and slight variations in the matrix should also be considered.
These additional uncertainties can be estimated, for example, from range control charts using test samples
of different matrices. All repeated measurements for the range control chart shall be subjected to a separate
sample preparation. For the calculation of the pooled standard deviation from these data, the procedure
specified in Annex B shall be used.
Since the uncertainty component from the range control chart, u , covers only the repeatability
r,range
component, it shall be combined with the uncertainty of the results from the quality control sample analysed,
i.e. the standard solutions, u , to obtain a reliable estimate of the within-laboratory reproducibility.
Rs, tand
w
uu=+ u (2)
R rr, ange
Rs, tand
w
w
where
u
is the uncertainty component of the results from the standard solution which is used as the
Rs, tand
w
quality control sample;
u is the uncertainty component from the range control chart.
r,range
The uncertainty component from the repeatability is partly included twice in this estimation, repeatability
from standard solutions (part of u ) as well as repeatability from quality control samples used in the
Rs, tand
w
range control chart. This leads to an overestimation. However, in general, the repeatability part of the
uncertainty component for the within-laboratory reproducibility, u , is small if measurements are
R
w
performed on standards at a concentration level well above the limit of quantification.
More double counting and therefore overestimation is included when the standard measurements for the
mean control chart include the sample preparation.
NOTE If there is a varying bias from day to day in the sample preparation (e.g. from varying contamination), this
contribution will not be included.
8.2.4 No stable quality control samples
Where no stable quality control samples are available, e.g. for the determination of oxygen in water, the
uncertainty component from the repeatability can be estimated from a pooled standard deviation of replicate
analyses (according to Annex B). For the first estimates of measurement uncertainty, see requirements for
the number of measurements in 8.2.1.
For the uncertainty component resulting from variations between days or analytical runs (e.g. from changes
in calibration or from changes in the state of the instruments), u , other procedures for the estimation
Rr, un
w
are required. In many cases, this component relies on scientific judgement based on the analyst’s experience
(see ISO/IEC Guide 98-3:2008, 4.3.1).
uu=+u (3)
Rr,range
Rr, un
w
w
where
u is the uncertainty component from the range control chart, see 8.2.3;
r,range
u
is the uncertainty component resulting from variations between analytical runs.
Rr, un
w
8.3 Bias
8.3.1 General
If possible, sources of bias should always be eliminated. ISO/IEC Guide 98-3 states that if bias is significant
and can be reliably estimated, then a measurement result should always be corrected. This is usually
specified during the development of a measurement procedure.
In many cases, the observed bias can vary depending on the matrix and the concentration of the analyte.
This can be taken into account by using several matrix reference materials.
To evaluate the uncertainty associated with bias, u , two components shall be estimated:
b
a) the bias itself (as difference from the nominal value or certified reference value);
b) the uncertainty of the nominal value or certified reference value.
NOTE The bias uncertainty component can be neglected if uu< /3 , because the contribution to the combined
b R
w
uncertainty then will be lower than 11 % calculated by error propagation.
In 8.3.2, 8.3.3 and 8.3.4, respectively, three approaches to estimating the uncertainty associated with bias
are outlined:
— analysis of suitable reference materials;
— participation in interlaboratory comparisons;
— recovery experiments with suitable samples.

8.3.2 Analysis of suitable reference materials
Results from regular analysis of suitable reference materials can be used to estimate the measurement
uncertainty component associated with bias, u . Each reference material should have been analysed in at
b
least six analytical runs.
NOTE 1 It is recognized that, while the analysis of the reference materials in at least six analytical runs is
appropriate for the vast number of situations, there are occasions when this is not so. The greater the number of
results, the greater the confidence in the estimation.
The uncertainty in the certified value of the certified reference material can be obtained from the producer’s
[6] [10]
certificate (see also ISO Guide 30 and ISO 17034 ). It can be necessary to convert the uncertainty given
on the certificate into a standard uncertainty, e.g. if the uncertainty is expressed as an expanded uncertainty
or as a confidence interval. For other reference materials, the uncertainty in the property value used as the
reference value can be taken from suitable statistical data, e.g. for material from interlaboratory trials from
the reproducibility standard deviation (see 8.3.3).
To obtain a reliable estimate of the measurement uncertainty component associated with bias, u , it is
b
advisable to use several reference materials covering the scope of the analytical method (different matrices
and concentration levels). If only one reference material is used, the uncertainty may be underestimated.
If several reference materials are used, different values for bias are obtained which are used to calculate the
uncertainty component b . The uncertainty component associated with bias, u , is given by:
rms b
uu=+b (4)
brms
C
ref
where
u
is the mean uncertainty of the reference values;
C
ref
b is the root mean square (quadratic mean) of the individual bias values, given by
rms
()b
∑ i
b = (5)
rms
n
r
where
th
b is the difference between the mean measured value and the accepted reference value of the i
i
reference material;
n is the number of reference materials.
r
If the individual bias values and the uncertainties of the reference values vary significantly, it can be
necessary to separately estimate uncertainties for the different cases.
If only one reference material is available, the results of analyses of this reference material are treated as the
best available estimate for the measurement uncertainty component associated with bias, u .
b
When only one reference material is used, the uncertainty component associated with bias is given by:
 
s
2 b 2
ub=+ +u (6)
 
b
  C
ref
n
 
M
where
b is the difference between mean measured value and an accepted reference value;
s is the standard deviation of the measured values of the reference material;
b
n is the number of bias measurements on the reference material;
M
u
is the uncertainty of the reference value.
C
ref
NOTE 2 If only one reference material is used, the uncertainty of the bias estimation sn/ can also make a
bM
significant contribution to u and is therefore included in Formula (6) (see Reference [11]).
b
8.3.3 Participation in interlaboratory comparisons
Results from interlaboratory comparisons can be used in a similar way as results from analyses of reference
materials, if it is assumed that the assigned value in the interlaboratory comparison is a sufficiently good
estimate of the true value.
NOTE 1 For each certified reference material, an estimate of bias, with a mean value based on several measurements
performed on different days, can be obtained. In proficiency testing schemes, often, only single measurements are
performed on a single day. Therefore, the difference between a laboratory result and the assigned value is calculated
for different interlaboratory samples. This difference then includes contributions from both the uncertainty
component associated with bias, u , and the uncertainty component for the within-laboratory reproducibility, u .
b R
w
The contributions from both components can lead to an overestimate of measurement uncertainty.
To determine an estimate of the bias from interlaboratory comparison results, a laboratory should have
analysed at least six different samples within one or more rounds of interlaboratory comparisons.
NOTE 2 It is recognized that, while the analysis of at least six different samples is appropriate for the vast number
of situations, there are occasions when this is not so. The greater the number of samples is, the greater the confidence
in the estimation.
The differences, D , between the measurement results and the assigned values for the different samples
i
can be both positive and negative. All difference values are used to estimate the root mean square of the
differences, D :
rms
D
∑ i
D = (7)
rms
n
ilc
where
th
D is the difference between the measurement result and the assigned value of the i sample of the
i
interlaboratory comparison;
n is the number of interlaboratory comparison samples analysed.
ilc
If the individual differences and the uncertainties of the assigned values vary significantly, it can be
necessary to separately estimate uncertainties for the different cases.
NOTE 3 Usually the uncertainty of an assigned value of an interlaboratory comparison sample is larger than the
uncertainty of the certified value of a certified reference material. Thus, usually the estimated uncertainty component
is larger. In some cases, the uncertainty of the assigned value of the interlaboratory comparison sample is so large that
it cannot be used for the estimation of the uncertainty component associated with bias.

If the provider of the interlaboratory comparison reports the uncertainty of the assigned value e.g. according
[12]
to the procedure described in ISO 13528 , then this should be used.
If no information is available from the provider, but it is known that the assigned value was derived from a
consensus mean of the participants’ results, calculated as either a robust or arithmetic mean, than the
th
uncertainty of the assigned value of the i interlaboratory sample, u , shall be estimated using
Ci,
ref
Formula (8) for each assigned value:
s
R,i
u =12, 5× (8)
Ci,
ref
n
p,i
where
u
is the uncertainty of the assigned value of the interlaboratory sample i;
Ci,
ref
s is the reproducibility standard deviation from the interlaboratory comparison for sample i;
R,i
n is the number of participating laboratories for sample i.
p,i
[12]
NOTE 4 As specified in ISO 13528, the factor of 1,25 is considered to be a conservative (high) estimate to account
for that proficiency testing results typically are not norm
...