8.10 Determination of the Measurement Uncertainty
131
of the combined uncertainty allows an independent and objective interpretation of
the results of testing. It can be also used for the metrological comparison of results
and, last but not least, to evaluate their quality and usefulness for the intended use.
For each of the parameters, their influence is on the analytical result should be
assessed and the value of the standard uncertainty should be calculated. A detailed
uncertainty budget can be therefore used for the optimization of the measurement
procedure aiming mainly for an analytical performance. The determination of the
combined standard uncertainty is based on the law of propagation, which means the
sum of the variance—that is, the square root of the values of the standard uncertainty. The breakthrough in the introduction of the uncertainty was the recognition
that when summing the variances, both the results obtained in the laboratory and
the manufacturer’s data should be included; for example, the purity of the reagents,
the uncertainty of the certified value or the previous experiences of the laboratory.
In relation to that, two methods of evaluating the uncertainty are distinguished: type
A and type B. The type A evaluation includes the statistical analysis of measured
results obtained under defined conditions; the components of the type A uncertainty
are expressed as a standard deviation with a known number of degrees of freedom.
The B type evaluation includes other data, determined by means other than statistical analysis. All the values belonging to the B type, before using the propagation
law, need to be reduced to the standard conditions—that is, to include statistical
coefficients and predicted distributions (normal, triangular, rectangular).
Type A evaluation of measurement uncertainty: evaluation of a component of
measurement uncertainty by statistical means.
Type B evaluation of measurement uncertainty: evaluation of a component of
measurement uncertainty by another means.
In practice, it means that the type A uncertainty has an experimental character
and it can be used when results of a series of measurements conducted in a laboratory with the help of a defined measuring procedure and in specified conditions
are available. The type B is of the calculation type and can be used when access to
credible information about the value of the uncertainty or another means of description of the spread of the values for a given quantity is available. Type B can be used
for the following information; for example, authorities published quantity values,
obtained from a calibration certificate, obtained from the accuracy class of a verified
measuring instrument.
In order to normalize all values to the standard deviation of type B, in practice, the
rectangular and triangular distributions are used. For example, the concentration of
a component of the solution provided by the manufacturer is 1000 mg/L ± 2 mg/L,
which means that the value can be found in the range 998–1002 mg/L. Taking into
consideration that, in such a case, the probability of occurrence of a result is equal in
the whole range, we take the rectangular distribution; hence the standard uncertainty
is 2/
√
3—that is, 1.16 mg/L.
131
of the combined uncertainty allows an independent and objective interpretation of
the results of testing. It can be also used for the metrological comparison of results
and, last but not least, to evaluate their quality and usefulness for the intended use.
For each of the parameters, their influence is on the analytical result should be
assessed and the value of the standard uncertainty should be calculated. A detailed
uncertainty budget can be therefore used for the optimization of the measurement
procedure aiming mainly for an analytical performance. The determination of the
combined standard uncertainty is based on the law of propagation, which means the
sum of the variance—that is, the square root of the values of the standard uncertainty. The breakthrough in the introduction of the uncertainty was the recognition
that when summing the variances, both the results obtained in the laboratory and
the manufacturer’s data should be included; for example, the purity of the reagents,
the uncertainty of the certified value or the previous experiences of the laboratory.
In relation to that, two methods of evaluating the uncertainty are distinguished: type
A and type B. The type A evaluation includes the statistical analysis of measured
results obtained under defined conditions; the components of the type A uncertainty
are expressed as a standard deviation with a known number of degrees of freedom.
The B type evaluation includes other data, determined by means other than statistical analysis. All the values belonging to the B type, before using the propagation
law, need to be reduced to the standard conditions—that is, to include statistical
coefficients and predicted distributions (normal, triangular, rectangular).
Type A evaluation of measurement uncertainty: evaluation of a component of
measurement uncertainty by statistical means.
Type B evaluation of measurement uncertainty: evaluation of a component of
measurement uncertainty by another means.
In practice, it means that the type A uncertainty has an experimental character
and it can be used when results of a series of measurements conducted in a laboratory with the help of a defined measuring procedure and in specified conditions
are available. The type B is of the calculation type and can be used when access to
credible information about the value of the uncertainty or another means of description of the spread of the values for a given quantity is available. Type B can be used
for the following information; for example, authorities published quantity values,
obtained from a calibration certificate, obtained from the accuracy class of a verified
measuring instrument.
In order to normalize all values to the standard deviation of type B, in practice, the
rectangular and triangular distributions are used. For example, the concentration of
a component of the solution provided by the manufacturer is 1000 mg/L ± 2 mg/L,
which means that the value can be found in the range 998–1002 mg/L. Taking into
consideration that, in such a case, the probability of occurrence of a result is equal in
the whole range, we take the rectangular distribution; hence the standard uncertainty
is 2/
√
3—that is, 1.16 mg/L.