Examples of Measurement
Uncertainty Budgets in Analytical Chemistry
For help with concepts you are welcome to visit the Online
Course of Measurement Uncertainty Estimation in Analytical Chemistry
For general guidance on the quality of analytical results see Accred. Qual.
Assur. 2015, 20, 229.
If you do not have online access to
the cited publications, please contact ivo.leito
ut.ee
Measurement
|
Complexity
of measurement
|
Elaboration
level
|
Extent
of comments
|
Description
|
Available files
|
Determination of
dissolved oxygen by electrochemical (amperometric) and optical
(luminescence-based) sensors
|
High |
High Performance characteristics
evaluated: drift, intermediate precision, accuracy of temperature
compensation, accuracy of reading (under different measurement conditions),
linearity, flow dependence of the reading, reading stability, matrix effects
of dissolved salts. |
High |
A comprehensive comparative validation for two different types of
dissolved oxygen (DO) analyzers, amperometric and optical, together with
estimation of measurement uncertainty is presented. The uncertainty
contributions of the main influencing parameters were estimated under
different experimental conditions. It was found that the uncertainties of
results for both analyzers are quite similar but the contributions of the
uncertainty sources are different. Our results imply that the optical analyzer might not be as robust as
is commonly assumed, however, it has better reading
stability, lower stirring speed dependence, and typically requires less
maintenance. On the other hand, the amperometric analyzer has a faster
response and wider linear range. |
Full text
of the article: I. Helm, G. Karina, L. Jalukse, T. Pagano, I. Leito, Environmental Monitoring and Assessment 2018, 190, 313 |
Oceanographic analysis:
determination of elements (Al, V, Fe, Cd) by ICP-MS in plankton matrix
|
High |
Medium (the Nordtest approach is used) |
The file is largely self-explanatory |
Uncertainty
is evaluated according to the Nordtest approach
using replicate measurements performed during ca 10 months with a CRM
(matrix: plankton). On every day all steps of the method were carried out
including sample preparation (via a literature method) and ICP-MS determination.
The random uncertainty component is evaluated via intermediate precision, the
systematic component is evaluated using the reference values of the CRMs.
Relative quantities are used. |
|
Determination of
acrylamide in snacks by LC-MS
|
High |
High |
High |
Measurement
uncertainty estimation of acrylamide determination in snacks by liquid
chromatography mass spectrometry (LC-MS) using the Nordtest approach. The
within-lab reproducibility component is evaluated as a standard deviation of
measurement results in a CRM (crisp bread) made over a time period of more
than a year. The bias component was evaluated from the results obtained with
two CRMs (crisp bread and potato snacks). |
XL
calculation files (initial and solved) as well as
a slideshow and a
video explaining the calculations: Determination of acrylamide in snacks by LC-MS |
Ammonium by Photometry
|
High |
Medium (somewhat simplified, suitable for
most labs) |
High |
A
mainstream measurement of NH4+ by photometry. The
measurement uncertainty (MU) estimation uses the simplification that slope
and intercept of the calibration graph are considered independent parameters. This is a
tricky example. After several years of discussion and careful study we now
believe that the MU in this example is not underestimated if the
determination is carried out carefully and if there is no strong chemical
interference. In any case, use with care! For deeper coverage of MU sources
in photometric analysis see the paper L.Soovali
et al Accred. Qual. Assur. 2006, 11, 246-255 and the PhD thesis of
Lilli Soovali (defended on June 20, 2006). |
The
example is explained in detail together with the ISO GUM modeling approach as
section 9 of the MU web course. Calculation of
the combined standard uncertainty using the Kragten approach is explained in section 9.7, where also the XL calculation
files (both initial and solved) are found. |
Ammonium by Photometry
|
High |
High (uncertainty estimated at full rigor,
suitable for experts) |
High |
The same
example as previous, solved in GUM Workbench with
full rigor. Contains XLS import. The corresponding SMU and XLS file must be
placed in the same folder. In case of problems, please use the PDF printout. |
In
English: |
Measurement uncertainty
in Kjeldahl nitrogen determination
|
Medium |
High |
High |
Determination
of protein content in food products by the photometric version of the Kjeldahl method (using the Digesdahl
sample mineralization equipment). The uncertainty is estimated using the
Nordtest approach. Within-lab reproducibility is estimated from a long-term
standard deviation of determination results with a standard sample. The bias
component is estimated using two CRMs. |
This
example is presented as three self-test exercises (with solutions and
explanations: finding the reproducibility component, finding the bias component, finding the combined standard uncertainty |
Measurement uncertainty
due to the matrix effect in LC-ESI-MS (LC-ESI-MSMS)
|
High |
High |
High |
This work
(A. Kruve, K. Herodes, I.
Leito. J. AOAC International 2010, 93, 306-314) presents an empirical approach - the matrix effect graph approach -
for estimating the uncertainty due to the matrix effect in LC-MS (with the
electrospray (ESI) ion source) analysis of pesticide residues in fruits and
vegetables. At certain time intervals (1 month), a calibration graph using
extracts of different fruits/vegetables as calibration solutions is prepared,
and a regression line is fitted through these data. These fruits/vegetables
may be either from the commodity group of the samples or from different
commodity groups. The relative residuals of the calibration point peak areas
are calculated and plotted against the measurement time - the matrix effect
graph is then obtained. The root mean square of the relative residuals is
calculated and used as the estimate of relative uncertainty of the sample
peak areas caused by the matrix effect. The matrix effect graph obtained over
fruits/vegetables from different commodity groups can also be used to
identify fruits/vegetables with extreme matrix effects. |
Full text of the article
(please contact us if you do not have online access to this article) |
Measurement uncertainty
of measurement with amperometric sensors
|
Medium |
High |
High |
This
tutorial review (I. Helm, L. Jalukse, I. Leito Sensors 2010, 10, 4430-4455)
focuses on measurement uncertainty estimation in amperometric sensors (both
for liquid and gas-phase measurements). The main uncertainty sources are
reviewed and their contributions are discussed with relation to the
principles of operation of the sensors, measurement conditions and properties
of the measured samples. The discussion is illustrated by case studies based
on the two major approaches for uncertainty evaluation - the ISO GUM modeling
approach and the Nordtest approach. This tutorial is expected to be of
interest to workers in different fields of science who use measurements with
amperometric sensors and need to evaluate the uncertainty of the obtained
results but are new to the concept of measurement uncertainty. The tutorial
is also expected to be educative in order to make measurement results more
accurate. |
Full text of the article (it is an open-access
article, so the full text is freely available) |
Electron probe microanalysis
(SEM-EDS)
|
High |
High |
High |
Determination
of iron in ink writing on paper manuscripts using electron probe
microanalysis (SEM-EDS). Full information, with detailed explanations on
uncertainty sources and their quantification is available in publication K.Virro
et al Microchimica Acta,
published online 06.08.2007. |
|
Analysis of gold alloys
by flame-AAS
|
High |
High |
High |
Detailed example,
covering not only uncertainty estimation but also validation and establishing
traceability |
Chapter 2 in Practical Examples on Traceability,
Measurement Uncertainty and Validation in Chemistry |
Determination of calcium
in serum by spectrophotometry
|
High |
High |
High |
Detailed
example, covering not only uncertainty estimation but also validation and
establishing traceability |
Chapter 3 in Practical Examples on Traceability,
Measurement Uncertainty and Validation in Chemistry |
Determination of radium
in water by a-spectrometry
|
High |
High |
High |
Detailed
example, covering not only uncertainty estimation but also validation and
establishing traceability |
Chapter 4 in Practical Examples on Traceability,
Measurement Uncertainty and Validation in Chemistry |
Determination of polar
pesticides by liquid chromatography mass spectrometry (LC-MS)
|
High |
High |
High |
Detailed
example, covering not only uncertainty estimation but also validation and establishing
traceability |
Chapter 5 in Practical Examples on Traceability,
Measurement Uncertainty and Validation in Chemistry |
Determination of
ammonium in water by flow analysis (CFA) and spectrometric detection
|
High |
High |
High |
Detailed
example, covering not only uncertainty estimation but also validation and
establishing traceability |
Chapter 6 in Practical Examples on Traceability,
Measurement Uncertainty and Validation in Chemistry |
Simple weighing
|
Simple |
Medium |
Medium |
Uncertainty
of simple weighing |
|
Volume of 50 ml
volumetric flask
|
Simple |
Medium |
Medium |
Uncertainty
of volume of solution contained in 50 ml volumetric flask. |
|
Volume of 10 ml pipette
|
Simple |
Medium |
Medium |
Uncertainty
of volume of solution delivered by 10 ml bulb pipette. |
|
Nonvolatile matter by
gravimetry
|
Medium |
Medium |
Medium |
Routine determination
of nonvolatile matter by gravimetry. The sample was weighed
before and after drying in oven at a specified temperature (please see
the presentation ISO
GUM Uncertainty in Chemistry). |
In
English: In
Estonian: |
pH measurement
|
Medium |
High |
Low |
The
uncertainty calculation for pH is available as a web application
(server-based, written in PHP). This means that calculation can be carried
out immediately in the browser and there is no need to install any software.
The result can be displayed either as a simple or as a detailed result. In
the latter case the measurement equation and detailed uncertainty budget are
also displayed. Additional information is available in the help file of the
web application and in the articles I.Leito,
L.Strauss, E.Koort, V.Pihl Accred. Qual. Assur. 2002, 7, 242-249 and E.Koort,
K.Herodes, V.Pihl, I.Leito. Anal. Bioanal. Chem. 2004,
379, 720-729. For more
information see also the PhD thesis of Eve Koort (defended on June 20, 2006). |
In
English: |
Dissolved oxygen
concentration measurement
|
Medium |
High |
High |
This
uncertainty estimation procedure is intended for the mainstream dissolved
oxygen concentration measurement with the galvanic type of equipment. Details
can be found in the article: L.Jalukse,
I.Leito Measurement Science and technology 2007,
18, 1877-1886 and also in the PhD thesis of Lauri Jalukse. |
In
English: |
Complexonometric titration
|
Medium |
Medium |
Medium |
Complexonometric determination (EDTA) of total hardness of water |
|
Nitrite by Photometry
|
High |
High |
High |
Photometric
determination of nitrite using the NEDA-sulfanilamide method. For deeper
coverage of MU sources in photometric analysis see the paper L.Soovali
et al Accred. Qual. Assur. 2006, 11, 246-255 and the PhD thesis of
Lilli Soovali (defended on June 20, 2006). |
|
Butanol in acetone by GC
|
High |
High |
Medium |
Measurement
of butanol content in acetone by GC. Very small solution volumes are used in
this method and all solutions are prepared by weighing. The largest
uncertainty contributions are due to the imperfections of integrating peaks
on the chromatogram and drift of the balance, which is mainly due to the
volatility of acetone. |
In
English: |
Sorbic acid by HPLC
|
High |
Low |
Medium |
Mainstream
liquid chromatography (HPLC) method for determination of preservatives
(Sorbic acid in this example). Main parameters of the method: Isocratic
elution (Acetate buffer : MeOH,
70:30), RP C18 column, UV-Vis photometric detection at 235 nm. |
In
English: In
Estonian: |
Quality control of a
drug product by HPLC
|
High |
High |
High |
Liquid
chromatography (HPLC) determination of Simvastatin in tablets. The method is
a mainstream HPLC method with UV-Vis photometric detection at 238 nm. Two
varieties are provided: 5-point calibration and single point calibration.
This uncertainty estimation has been published in the following paper: S. Leito et al J. Chrom. A 2006, 1121, 55-63. |
In
English: 5-point
calibration: Single-point
calibration: |
Phosphorus Content in
Feed by Photometry
|
High |
High |
High |
Measurement
uncertainty estimation example on photometric determination of phosphorus in
feed using the molybdatovanadate reagent. The
largest uncertainty contribution is due to the sample preparation. For deeper
coverage of MU sources in photometric analysis see the paper L.Soovali
et al Accred. Qual. Assur. 2006, 11, 246-255 and the PhD thesis of
Lilli Soovali (defended on June 20, 2006). |
|
Lead in Soil by AAS
|
High |
High |
High |
Measurement
of Lead content of soil by graphite furnace atomic absorption spectrometry. |
Comments
Files
|
The
uncertainty budgets are available in files of following types:
Most of
the files are in English. In some cases files in other languages are also
available. |
Complexity, elaboration
level and extent of comments
|
The "complexity of measurement" refers to the intrinsic
complexity of the measurement itself (the more there are operations and
measurements, the higher the complexity) The "elaboration level" refers to the extent to which
various uncertainty sources have been identified and taken into account. Low
elaboration level does not necessarily mean that there are important
uncertainty sources that have not been taken into account: instead it usually
means that here and there several different uncertainty sources have been
grouped. For example, instead of identifying all the repeatability
contributions, they may have been grouped to give the general repeatability
of the procedure that can be estimated from overall repeatability studies. The "extent of comments": indicates how much comment is
added to the file to increase the readability by users. |
Estimates of uncertainty
components
|
Generally
the uncertainty components have been estimated according to the particular
equipment and working practices used in our lab (or in the labs of our
collaborators). In some cases reasonable estimates (based on experience or
literature data) are used. The obtained uncertainty values have proved to be
adequate for those conditions. However, these uncertainty values are not
directly applicable to results obtained in other laboratories using different
instrumentation and working practices (even if exactly the same measurement
procedures are used) because they are dependent on the conditions. These
values should thus be used for guidance only. The users of the examples are
strongly recommended to do their own estimation of uncertainty components
based on their own equipment and working practices and then insert the
uncertainty data into the files from this page. Also, it is strongly
recommended to see the Online Course of Measurement
Uncertainty Estimation in Analytical Chemistry. |
Feedback
|
Any
feedback (comments, error reports, criticism) is most welcome! The feedback
should be sent to Ivo Leito (ivo.leito[at]ut.ee, +372 5 184 176, University of Tartu, Testing Centre, Ravila
14a, 50411 Tartu, Estonia). You can also submit your own examples for posting
on this site. The examples will be examined and then decision will be made,
whether they are suitable. Preference will be given to detailed and fully
commented examples. |
Other topics
|
See also
other research topics |
|
This page has been created at University of
Tartu with support from the EC JRC Institute for Reference Materials and
Measurements in the framework of the TrainMiC
programme. |
Last edited: 06.11.18