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8 Measurement Uncertainty
8.12 Modeling According to the ISO GUM Guide
The process of evaluation of uncertainty, according to ISO GUM guide (‘Guide to
the Expression of Uncertainty in Measurement’) includes the following steps:
1. Determination of the measuring procedure and the measured quantity.
The quantity of interest in a given measurement should be clearly defined, and
the unit for the expression of final results should be selected.
2. Description of the measuring procedure in the form of a mathematical equation
(model).
The model equation is a mathematical description of the dependency of the value
of the determination result and the measured values. That dependency has the
form of the equation:
y f (x 1 , x 2 , . . . X n )
(8.10)
where y is output quantity; x 1 , x 2 , …, x n are input quantities.
3. Identification of factors that influence the measurement result (uncertainty).
All identified sources of uncertainty—those that influence the measurement—should cover all factors that affect measurement results. Those could include,
for example, the recovery of the analyte from the sample, the conditions of sample storage, the purity of the used reagents, stoichiometry of the reactions, the
conditions in which the measurements are conducted, the precision of the measurements, the stability of the measuring device, the resolution of the measuring
device, the quality of the standards used (i.e. the uncertainty of the certified
value).
4. Assigning the source of uncertainty to type A or B (for the purpose of normalization to standard uncertainty).
Uncertainty components can be divided into two categories, depending on the
method of calculating their numerical values.
Type A—can be calculated with the use of statistical methods (they are characterized by estimates of the standard deviation and the number of the degrees of
freedom); these are the quantities whose values and uncertainties can be determined
on the basis of the results of measurements conducted in the laboratory.
Type B—have been determined not by statistical means (they are characterized
by the approximate estimates of the standard deviation); these are the quantities
whose values and uncertainties have been entered into the measurement from sources
other than statistical ones (e.g., calibration certificates, certificates of the reference
materials, tables).
This classification is not connected with the different nature and/or properties of
the components of uncertainty, nor with their indication; it is only a way to determine
the way to normalize all values into the standard uncertainty. For uncertainty of
the type A, the estimate of the standard deviation is calculated from the repeated
measurements; for the type B, the available data, other than the measuring ones are
used.
8 Measurement Uncertainty
8.12 Modeling According to the ISO GUM Guide
The process of evaluation of uncertainty, according to ISO GUM guide (‘Guide to
the Expression of Uncertainty in Measurement’) includes the following steps:
1. Determination of the measuring procedure and the measured quantity.
The quantity of interest in a given measurement should be clearly defined, and
the unit for the expression of final results should be selected.
2. Description of the measuring procedure in the form of a mathematical equation
(model).
The model equation is a mathematical description of the dependency of the value
of the determination result and the measured values. That dependency has the
form of the equation:
y f (x 1 , x 2 , . . . X n )
(8.10)
where y is output quantity; x 1 , x 2 , …, x n are input quantities.
3. Identification of factors that influence the measurement result (uncertainty).
All identified sources of uncertainty—those that influence the measurement—should cover all factors that affect measurement results. Those could include,
for example, the recovery of the analyte from the sample, the conditions of sample storage, the purity of the used reagents, stoichiometry of the reactions, the
conditions in which the measurements are conducted, the precision of the measurements, the stability of the measuring device, the resolution of the measuring
device, the quality of the standards used (i.e. the uncertainty of the certified
value).
4. Assigning the source of uncertainty to type A or B (for the purpose of normalization to standard uncertainty).
Uncertainty components can be divided into two categories, depending on the
method of calculating their numerical values.
Type A—can be calculated with the use of statistical methods (they are characterized by estimates of the standard deviation and the number of the degrees of
freedom); these are the quantities whose values and uncertainties can be determined
on the basis of the results of measurements conducted in the laboratory.
Type B—have been determined not by statistical means (they are characterized
by the approximate estimates of the standard deviation); these are the quantities
whose values and uncertainties have been entered into the measurement from sources
other than statistical ones (e.g., calibration certificates, certificates of the reference
materials, tables).
This classification is not connected with the different nature and/or properties of
the components of uncertainty, nor with their indication; it is only a way to determine
the way to normalize all values into the standard uncertainty. For uncertainty of
the type A, the estimate of the standard deviation is calculated from the repeated
measurements; for the type B, the available data, other than the measuring ones are
used.