134
8 Measurement Uncertainty
8.11 Evaluation of Uncertainty: Requirements in Chemical
Measurements
The procedure of determination of measurement uncertainty, described in the ISO
GUM guide is commonly recognized. The ISO GUM procedure is often called as
‘modeling,’ as the main requirement is the establishing of a mathematical equation
(model) that describes the measuring process. In practice, the mathematical model
is an equation that is used to calculate the measurement result. It is assumed that
all constituents of that equation (input quantities) are parameters that influence the
value of the measurement result, and thus they influence the measurement uncertainty.
Therefore, for each input quantity, their values need to be assessed and the estimates
of their uncertainties need to be provided. After normalizing all uncertainties to their
standard values, the combined standard uncertainty should be calculated, using the
law of propagation. The final step is the calculation of the expanded uncertainty for
the specific confidence level.
The procedure of evaluation of measurement uncertainty, described in the ISO
GUM guide, does not require knowledge of very advanced statistical methods. In
reality, only basic information is necessary to conduct all the required calculations.
The most important ones include knowledge of the propagation law and the ability
to use different statistical distributions. When calculating the constituent values to
standard uncertainties, it is necessary to be able to choose the type of distribution
that a given value is subject to. It must be remembered that the type of distribution
(normal, rectangular, triangular) influences the transformation of a given value into
the standard form. This particularly applies to the type B uncertainty (e.g., archival
measurement data, manufacturer data, literature data).
Typically, the process of uncertainty evaluation includes following steps:
– Specify the measurand;
– Specify the measurement procedure and describe the measurement model (equation);
– Identify the sources of uncertainty;
– Assign the numerical values to the uncertainty components;
– Calculate the combined standard uncertainty;
– Calculate the expanded uncertainty (with a given coverage factor, k);
– Examine the uncertainty budget.
This is how one can outline the basic scenario for determining the uncertainty in
accordance with the procedure described in the ISO GUM guide. Since this document
has been published, discussions have been conducted among the chemist community
on the possibility of using the mathematical model to describe all steps of the measurements procedure. In chemical measurements, it is not always possible to describe
the entire procedure in the form of a mathematical model and hence great effort was
taken to develop a non-mathematical way to evaluate uncertainty (Table 8.1). In practice, a good alternative are those processes that use experimental data; often those are
8 Measurement Uncertainty
8.11 Evaluation of Uncertainty: Requirements in Chemical
Measurements
The procedure of determination of measurement uncertainty, described in the ISO
GUM guide is commonly recognized. The ISO GUM procedure is often called as
‘modeling,’ as the main requirement is the establishing of a mathematical equation
(model) that describes the measuring process. In practice, the mathematical model
is an equation that is used to calculate the measurement result. It is assumed that
all constituents of that equation (input quantities) are parameters that influence the
value of the measurement result, and thus they influence the measurement uncertainty.
Therefore, for each input quantity, their values need to be assessed and the estimates
of their uncertainties need to be provided. After normalizing all uncertainties to their
standard values, the combined standard uncertainty should be calculated, using the
law of propagation. The final step is the calculation of the expanded uncertainty for
the specific confidence level.
The procedure of evaluation of measurement uncertainty, described in the ISO
GUM guide, does not require knowledge of very advanced statistical methods. In
reality, only basic information is necessary to conduct all the required calculations.
The most important ones include knowledge of the propagation law and the ability
to use different statistical distributions. When calculating the constituent values to
standard uncertainties, it is necessary to be able to choose the type of distribution
that a given value is subject to. It must be remembered that the type of distribution
(normal, rectangular, triangular) influences the transformation of a given value into
the standard form. This particularly applies to the type B uncertainty (e.g., archival
measurement data, manufacturer data, literature data).
Typically, the process of uncertainty evaluation includes following steps:
– Specify the measurand;
– Specify the measurement procedure and describe the measurement model (equation);
– Identify the sources of uncertainty;
– Assign the numerical values to the uncertainty components;
– Calculate the combined standard uncertainty;
– Calculate the expanded uncertainty (with a given coverage factor, k);
– Examine the uncertainty budget.
This is how one can outline the basic scenario for determining the uncertainty in
accordance with the procedure described in the ISO GUM guide. Since this document
has been published, discussions have been conducted among the chemist community
on the possibility of using the mathematical model to describe all steps of the measurements procedure. In chemical measurements, it is not always possible to describe
the entire procedure in the form of a mathematical model and hence great effort was
taken to develop a non-mathematical way to evaluate uncertainty (Table 8.1). In practice, a good alternative are those processes that use experimental data; often those are