Instrumentation & Measurement Magazine 24-1 - 48

Fig. 6. The correct version of the incorrect Fig. 5.

Fig. 4. This correct visualization has also been used by some authors.

represented by the blue curve. Let us assume that the figure
corresponds to results returned by a measurement instrument,
and not measurements and their results. Fig. 5(i) still has three
problems:
1.	It reports the offset of Vm (the average of the distribution) from the reference value Vref as accuracy, instead of
trueness.
2.	It conveys the message that the greater the distance
between Vm and Vref, the greater the accuracy, which in
fact is the exact opposite!
3.	Similarly, it conveys the message that the greater the
distance between Vmin and Vmax, the greater the precision,
which in fact is the exact opposite!
Fig. 5(ii) has the same problem (3), as well as problem (2)
but for trueness instead of accuracy.

Fig. 6 shows the corrected version of this form of visualization, which refers to components of errors, again under the
assumption that a reference value is somehow known. Notice
that we have also changed the label of the vertical axis from
" probability density " to " probability distribution, " because
" density " implies the continuity of values, while measurement
values are defined on a discrete scale due to finite resolution of
measuring instruments.
Concluding, let us reiterate that accuracy should be part of
the characterization of a measurement instrument but not part
of the characterization of measurement results, since evaluating accuracy requires a reference value to be known, which
is not the case for measurement results. In this latter case,
measurement uncertainty is the feature that summarizes the
distribution of measured values. According to the Guide to the
Expression of Uncertainty in Measurement (GUM), measurement
uncertainty is a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could
reasonably be attributed to the measurand [3, 2.2.3].
In general, measurement uncertainty comprises several
components that may manifest themselves with either random

Fig. 5. Another form of incorrect visualization.
48	

IEEE Instrumentation & Measurement Magazine	

February 2021



Instrumentation & Measurement Magazine 24-1

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