120
8 Measurement Uncertainty
Target measurement uncertainty: measurement uncertainty specified as an
upper limit and decided on the basis of the intended use of the measurement
results.
clause 2.34; ISO/IEC Guide 99
Thus, in VIM 3, two terms related to the measurement uncertainty and regarding
reliability and the usefulness of the measurement result are introduced. The term
‘definitional uncertainty’ means, in practice, the minimum measurement uncertainty
achievable in any measurement in a given measurand.
In literature, the terms ‘definitional uncertainty’ or ‘basic uncertainty’ can also
be encountered. In practice, this means that taking into consideration all the steps of
a given measuring procedure and including all components of the uncertainty, the
result cannot be obtained with a smaller uncertainty than the definitional uncertainty.
The term ‘target measurement uncertainty,’ on the other hand, refers to the upper
limit of the uncertainty that is acceptable for a specific use of the measurement result.
In practice, this means that a useful result is one that has an assigned uncertainty that
does not exceed the specified target uncertainty.
8.3 Measurement Results
By conducting a series of measurements in the conditions of repeatability, one obtains
a set of raw data, the variability of which is a reflection of the random error. Admittedly, the error is a very useful term for understanding the rules and basics of the
measurement uncertainty evaluation; however, its practical meaning is limited due
to the lack of ability to determine the error for the given measurement. This stems
from the fact that the true value of the measured quantity is unknown. In practice,
the term ‘reference value’ is used; this is a value assigned to the determined quantity
and recognized—sometimes arbitrarily—as the value determined with acceptable
uncertainty for the specific use.
For the assessment of the numerical values obtained as the result of conducted
measurements, it is accepted to use several terms and theorems of the theory of
probability. In accordance with it, every measurement result is a random variable and
the best model of a random variable is its probability spread. To describe the random
variables, most often the expected value (μ) and the standard deviation (σ ) are used.
In practice, the values of those parameters are not known, and they are estimated on
the basis of a series of experimental tests, and those are called estimators.
The expected value μ, which corresponds to the true value, is estimated by calculating its estimator from the results of the test, which is the mean value X mean.
In mathematical notation, if each result is noted as X i , i 1, 2, …, n; where n is the
number of results, then the mean value is calculated on the basis of the dependency:
8 Measurement Uncertainty
Target measurement uncertainty: measurement uncertainty specified as an
upper limit and decided on the basis of the intended use of the measurement
results.
clause 2.34; ISO/IEC Guide 99
Thus, in VIM 3, two terms related to the measurement uncertainty and regarding
reliability and the usefulness of the measurement result are introduced. The term
‘definitional uncertainty’ means, in practice, the minimum measurement uncertainty
achievable in any measurement in a given measurand.
In literature, the terms ‘definitional uncertainty’ or ‘basic uncertainty’ can also
be encountered. In practice, this means that taking into consideration all the steps of
a given measuring procedure and including all components of the uncertainty, the
result cannot be obtained with a smaller uncertainty than the definitional uncertainty.
The term ‘target measurement uncertainty,’ on the other hand, refers to the upper
limit of the uncertainty that is acceptable for a specific use of the measurement result.
In practice, this means that a useful result is one that has an assigned uncertainty that
does not exceed the specified target uncertainty.
8.3 Measurement Results
By conducting a series of measurements in the conditions of repeatability, one obtains
a set of raw data, the variability of which is a reflection of the random error. Admittedly, the error is a very useful term for understanding the rules and basics of the
measurement uncertainty evaluation; however, its practical meaning is limited due
to the lack of ability to determine the error for the given measurement. This stems
from the fact that the true value of the measured quantity is unknown. In practice,
the term ‘reference value’ is used; this is a value assigned to the determined quantity
and recognized—sometimes arbitrarily—as the value determined with acceptable
uncertainty for the specific use.
For the assessment of the numerical values obtained as the result of conducted
measurements, it is accepted to use several terms and theorems of the theory of
probability. In accordance with it, every measurement result is a random variable and
the best model of a random variable is its probability spread. To describe the random
variables, most often the expected value (μ) and the standard deviation (σ ) are used.
In practice, the values of those parameters are not known, and they are estimated on
the basis of a series of experimental tests, and those are called estimators.
The expected value μ, which corresponds to the true value, is estimated by calculating its estimator from the results of the test, which is the mean value X mean.
In mathematical notation, if each result is noted as X i , i 1, 2, …, n; where n is the
number of results, then the mean value is calculated on the basis of the dependency: