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Uncertainty is always a hot topic, not only for the metrology community, but also for technology and global trade because all results of measurements must contain according to international
standards an “expression of uncertainty in measurement”. This
is of central importance for all applications of measurement results, from engineering to chemistry and to the life sciences.
However, the word “un-certainty” may imply for non-metrologists – for example a lawyer who uses “measurement results with uncertainties” in a court procedure – that measurement results are “not” certain. To avoid such misconceptions,
the metrological uncertainty should be supplemented by expressions illustrating the “certainty” of measurement results – accuracy, trueness, precision may be appropriate in this respect.
The master document, which is acknowledged to apply to all
measurement and testing fields and to all types of uncertainties
of quantitative results, is the well-known Guide to the Expression
of Uncertainty in Measurement (GUM). The essential points of
the “GUM uncertainty philosophy” are:
"##A measurement quantity, of which the true value is not
known exactly, is considered as a stochastic variable with a
probability function. Often it is assumed that this is a normal
(“Gaussian”) distribution.
"##The result x of a measurement is an estimate of the expectation value.
"##Expectation (quantity value) and standard uncertainty are estimated either
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by statistical processing of repeated measurements (Type A
Uncertainty Evaluation) or
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by other methods (Type B Uncertainty Evaluation)
"##The result of a measurement has to be expressed as a quantity
value together with its uncertainty, including the unit of the
measurand.
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Since the 1990s there has been a conceptual change from the
traditionally applied Error Approach to the Uncertainty Approach.
In the Error Approach it is the aim of a measurement to determine an estimate of the true value that is as close as possible
to that single true value. In the Uncertainty Approach it is assumed that the information from measurement only permits
assignment of an (max – min) interval ! of reasonable values
to the measurand.
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The GUM requests to consider all components that contribute to the measurement uncertainty of a measured quantity.
The various uncertainty sources and their contributions can be
divided into four major groups, as has been proposed by the
EUROLAB Guide to the Evaluation of Measurement Uncertainty for
Quantitative Test Results (2006).
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• the sample being not completely representative
• inhomogeneity effects
• contamination of the sample
• instability / degradation of the sample or#other effects during
sampling, transport, storage etc.
• the sub-sampling process for the measurement (e.g. weighing)
• the sample preparation process for the measurement (dissolv-
ing, digestion)
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• instability of the investigated object
• degradation / ageing
• inhomogeneity
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be evaluated using statistical methods, e.g. the experimental
standard deviation of a mean value (Type A evaluation according to GUM).
Systematic errors result in the center of the distribution being shifted away from the true value by a distance S even in
the case of infinite repetitions. If systematic effects are known,
they should be corrected for in the result, if possible. Remaining systematic effects must be estimated and included in the
measurement uncertainty.
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• matrix effects and interactions
• extreme values, e.g. small measured quantity / little con-
centration
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• the definition of the measurand (approximations, idealizations)
• non-linearities, extrapolation
• different perception or visualization of measurands (different experimenters)
• uncertainty of process parameters (e.g. environmental conditions)
• neglected influence quantities (e.g. vibrations, electromagnetic fields)
• environment (temperature, humidity, dust, etc.)
• limits of detection, limited sensitivity
• instrumental noise and drift
• instrument limitations (resolution, dead time, etc.)
• data evaluation, numerical accuracy etc.
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• uncertainties of certified values
• calibration values
• drift or degradation of reference values / reference materials
• uncertainties of inter-laboratory comparisons
• uncertainties from data used from the literature
All possible sources for uncertainty contributions need to be
considered, when the measurement uncertainty is estimated,
even if they are not directly expressed in the measurement
function.
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In the traditional Error Approach a clear distinction was made
between so-called “random errors” and “systematic errors.” Although this distinction is not relevant within the uncertainty
approach anymore as it is not unambiguous, the concept is
nevertheless descriptive.
Random effects contribute to the variation of individual results in replicate measurements. Associated uncertainties can
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These terms, defined in the International Standard ISO 3534,
are characterizing a measurement procedure and can be used
with respect to the associated uncertainty.
• Accuracy as an umbrella term characterizes the closeness of
agreement between a measurement result and the true value
of a measurand. If several measurement results are available
for the same measurand from a series of measurements, accuracy can be split up into trueness and precision.
• Trueness accounts for the closeness of agreement between
the mean value and the true value.
• Precision describes the closeness of agreement of the individual values themselves.
The target model visualizes comprehensively the different
possible combinations, which result from true or wrong and
precise or imprecise results. It may be concluded that in order
to avoid misconceptions of the metrological term uncertainty,
the target model and the items accuracy, trueness, precision,
can be helpful.
This Letter originates from the Chapter Uncertainty and Accuracy
of Measurement and Testing (by Anita Schmidt, Manfred Golze
and Horst Czichos) of the Springer Handbook of Metrology
and Testing, Springer 2011.
[email protected]
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