We know that measurement is the set of operations aimed at determining the value of a quantity. However, these operations are inevitably affected by errors that affect the quality of the measurement made. The error that is committed is obviously the result of multiple errors that have different origins and entities and that can act individually or simultaneously.
Types of errors
We can therefore divide these errors into:
- Known : qualitatively and therefore a correction can be made to the value of the measurand;
- Unknown : which are not predictable or which one does not want to predict for cost reasons, therefore they cannot be eliminated and they determine the quality of the measurement.
The VIM (International Vocabulary of basic and general terms in Metrology) defines error (or absolute error) as:
“difference between the measured value and the (conventionally) true value of the measurand.”
And a =V m -V v
E a : absolute error
V m : measured value
V v: true value
From this we can define what we call relative error, that is, the ratio between absolute error and the mean value of the series of measurements.
And r =E a /V ?
E r : relative error ;
V ?: average value .
Relative error arises from the need to verify whether an error is small or large by comparing it with the value of the measurement itself; the lower the value of the relative error, the greater the precision of the measurement taken.
From this we can also define the percentage error, that is, the relative error reported in percentage notation:
And p =E r ?100
And p : percentage error
In metrology, however, we know that a quantity is never perfectly defined, so it is not possible to give it an absolute (true) value. Given the impossibility of giving a unique value to the measurement, it is not possible to define an error in these terms.
In order to continue to use the definitions written above, we must therefore understand what is meant by ‘true’ value. In metrology, therefore, absolute error means the difference between the measured value and the average value of the experimental data.
Over time, however, it has been seen that the statistical approach is more functional to measurements, which is why the concept of measurement uncertainty was born. That is, we can attribute an average or nominal value to the measurand and associate an uncertainty that defines its dispersion around that average value.
