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8 Measurement Uncertainty
the limits of that range. The term ‘the correctness of the measurement’ is understood
as the compatibility between the mean value determined for a measurement series
(Attention! In the VIM 3 dictionary it is referred to as “from an indefinite number
of repeated values of the measured quantities”) and the reference values. Hence, the
question arises: how we can determine and/or classify the correctness of the measurements? According to the metrological principles, the correctness of the measurement
is concluded on the basis of the uncertainty assigned to it.
The evaluation of the measurement correctness is one of the basic issues of
metrology, as it defines the comparability, reliability and usefulness of the
results.
According to the definition from the ISO GUM guide and the VIM 3 dictionary,
uncertainty is understood as a non-negative parameter that characterizes the spread
of the values that can, in a justifiable way, be assigned to the measured quantity.
The measurement error, on the other hand, is the difference between the result of the
measurement and the reference value of the measured quantity. The measurement
error is a good indicator of the degree of compliance of the measurement result
with the reference value, which is an indicator of the measurement correctness. The
reference value is used for comparison with the measured values for a given quantity
(object property). In chemical measurements, the reference value can be the certified
value specified on the certificate of the certified reference material, the value from
the certificate of the chemical standard of the pure substance, as well as the value
obtained with the reference measurement procedure.
The absolute error ΔX: the difference between the measured value X and the
reference value X R ; both are expressed in the unit of the measured value.
X X − X R
(8.1)
The relative error δX (expressed in percentage): the ratio of the absolute error
ΔX to the reference value multiply by 100%
X X − X R / X · 100%
(8.2)
Let us assume that during the measurement of the X p quantity, the result X was
obtained. According to the axiom of the metrology, it can be noted that X X p . It
is, therefore, necessary to complete the X result with the value of the parameter that
characterizes the expected range of the results variability, connected to their random
8 Measurement Uncertainty
the limits of that range. The term ‘the correctness of the measurement’ is understood
as the compatibility between the mean value determined for a measurement series
(Attention! In the VIM 3 dictionary it is referred to as “from an indefinite number
of repeated values of the measured quantities”) and the reference values. Hence, the
question arises: how we can determine and/or classify the correctness of the measurements? According to the metrological principles, the correctness of the measurement
is concluded on the basis of the uncertainty assigned to it.
The evaluation of the measurement correctness is one of the basic issues of
metrology, as it defines the comparability, reliability and usefulness of the
results.
According to the definition from the ISO GUM guide and the VIM 3 dictionary,
uncertainty is understood as a non-negative parameter that characterizes the spread
of the values that can, in a justifiable way, be assigned to the measured quantity.
The measurement error, on the other hand, is the difference between the result of the
measurement and the reference value of the measured quantity. The measurement
error is a good indicator of the degree of compliance of the measurement result
with the reference value, which is an indicator of the measurement correctness. The
reference value is used for comparison with the measured values for a given quantity
(object property). In chemical measurements, the reference value can be the certified
value specified on the certificate of the certified reference material, the value from
the certificate of the chemical standard of the pure substance, as well as the value
obtained with the reference measurement procedure.
The absolute error ΔX: the difference between the measured value X and the
reference value X R ; both are expressed in the unit of the measured value.
X X − X R
(8.1)
The relative error δX (expressed in percentage): the ratio of the absolute error
ΔX to the reference value multiply by 100%
X X − X R / X · 100%
(8.2)
Let us assume that during the measurement of the X p quantity, the result X was
obtained. According to the axiom of the metrology, it can be noted that X X p . It
is, therefore, necessary to complete the X result with the value of the parameter that
characterizes the expected range of the results variability, connected to their random