Measurement uncertainty

How do we know if instruments indicate the right values?

No single measurement is 100% accurate. Every measurement has its so called measurement uncertainty. Measurement uncertainty is a difficult and a poorly understood topic. This article aims to explain this subject and its problems in an easy way, based on an example.

To measure is to know?

In order to perform measurements, instruments are used. This can be as simple as a balance or a ruler or as complex as a measurement receiver or a gas chromatograph. No single instrument, no matter how expensive, is 100% accurate. This is, in fact, a physical law. So, how do we know that a measurement instrument indicates the correct value and how do we know the deviation of the instrument? Firstly this has to do with the application of the instrument, the purpose for which we select the instrument. For instance it is of no use to select a 6 digit volt meter to use it to measure the main supply. On the other hand a 3 digit volt meter is not suitable to measure voltages produced by brain activity. Every measuring purpose requires the right instrument with its own set of specifications.


Imagine we have selected an instrument fit for its purpose. Do we know for sure this instrument will provide us with the correct values? The answer to this question is negative. First of all we have to define "correct value". In the end an absolute exact value does not exist. We have to deal with so called "uncertainty". Lets for example look at time. Apart from relativity the best precision to be obtained is 10 to power -17 (10-17). National standards obtain an accuracy of 10-13. However accurate, there always remains an uncertainty. The deviation from the instrument itself can be determined by performing a calibration with an instrument that itself has a lower deviation than the instrument that is calibrated. This way a pyramid of uncertainties is created where the top has the least uncertainty while this increases to the bottom. This is also called traceability of the calibration to higher (international) standards. According to the European definition of calibration, the instrument is not corrected or adjusted. Only the deviation from the "exact" value is determined including its accompanying uncertainty. This deviation can then be used during measurements to correct the obtained value.


The inaccuracy of the measurement instrument is not the only contributor to the total measurement uncertainty. From that perspective the determination of the measurement uncertainty is an unsatisfactorily activity: The more ones does its best the worse the final result will be. An extreme low uncertainty is more often than not the result of "forgotten contributions" than of a high technical competence. When we speak about contributions to the measurement uncertainty, one has to think not only about the calibration setup but also the differences that are due to the tightening of connectors, the environmental conditions (radiation, temperature, humidity etc.) and the competence of the calibration engineer and many other factors.

The contributions can be added in different ways. The correct way to add contributions depends on the fact whether the contributions are correlated. The most used way of addition is the root mean square (RMS) method.

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