What is measurement uncertainty?
The uncertainty of the result of a measurement reflects the lack of knowledge about the true value of the measurand.
In the field of metrology, uncertainty is a non-negative parameter that characterizes the dispersion of the values attributed to a measurand, based on the information used (VIM, International Vocabulary of Metrology).
According to the definition of the Guide for the Expression of Measurement Uncertainty GUM, uncertainty is the “parameter associated with the result of a measurement, which characterizes the dispersion of the values that can reasonably be attributed to the measurand.”
In general terms, when performing a measurement or a series of measurements, a value is always obtained that is not true, that is, there is an uncertainty about how true the value obtained in the measurement is or not. This uncertainty is expressed as a value associated with that measurement or series of measurements and which must be quantified. Keeping in mind that there is always a margin of doubt in any measurement, it is necessary to know how large that margin is. Therefore, when expressing the result of the measurement of a physical quantity, it is necessary to give some quantitative indication of the quality of said measurement, or of the confidence we have in it, which establishes how sure we are that the “true value” is within that margin.
That measurement result must generally be expressed as a single measured value and a measurement uncertainty that is expressed as an interval, “±”. A calibration certificate from an accredited laboratory must always express the measurement results in this way. For example: If the estimation of the most probable measured result (y) and the uncertainty (U) have been made correctly, the probability that the true value of that measured physical quantity is in the interval y ± U will be high (usually 95%).
If we say that the length of a certain bar measures 20 cm (y), plus or minus ± 1 cm (U), with 95% confidence, we can express it like this: 20 cm ± 1 cm, with a confidence level of 95%. This means that in 95 out of 100 measurements the length of the bar is between 19 and 21 centimeters.
Uncertainty is often confused with measurement error.
- Error: Difference between a measured value and the conventionally true value of the object being measured.
- Uncertainty: Quantification of the doubt that one has about the result of that difference obtained in the measurement.
When possible, we try to correct known errors, but any error whose value is not known is a source of uncertainty.
Types of uncertainty
According to the GUM we can group the uncertainty components into two categories according to the evaluation method; “type A” and “type B”. The classification into type A and type B does not imply any difference in nature between the components of these types, it consists only of two different ways of evaluating the uncertainty components, and both are based on probability distributions.
- Type A: These are those obtained from statistical data.
- Type B: These are those obtained from scientific data or other sources.
How is uncertainty estimated or quantified?
We could not explain mathematically how the uncertainty of the measurement is estimated here. The GUM gives it a very broad and quite complicated treatment on how to estimate it. Extensive knowledge of statistics and mathematics is required, but we can clarify how uncertainty is composed.
In a series of measurements there are several factors and/or sources that contribute to the estimation of uncertainty. Every doubt that can be had and quantified specifically related to a measurement carried out and that affects the result of the measurement is a source of uncertainty.
In this order of ideas we would have sources of uncertainty related to the object to be measured, to the reference or standard measurement and to the measurement carried out. Additionally, uncertainty can also be generated by the laboratory where the measurement is made and the place where the measurement is made. From this, the sources of uncertainty in the calibration of a manometer can be the following (and we say they can be because it is not the law that those mentioned below are the only ones).
A laboratory can generate and identify different sources of uncertainty.
Sources of uncertainty related or attributed to the instrument to be calibrated:
a. The resolution.
b. Deviation from zero.
Sources of uncertainty related or attributed to the reference or standard measurement:
a. Pattern uncertainty.
b. Pattern drift.
Sources of uncertainty related to or attributed to the calibration performed:
a. Repeatability according to DKD R6-1.
b. Hysteresis according to DKD R6-1.
c. Reproducibility according to DKD R6-1.
Sources of uncertainty related to or attributed to the location where the calibration is performed:
a. Environmental conditions.
Sources of uncertainty related to or attributed to the laboratory performing the calibration:
a. Testbench column difference.
b. Laboratory reproducibility according to proficiency tests.
Each of these sources of uncertainty is treated or evaluated differently depending on whether they are Type A or Type B.
- Type A: Uncertainty is determined through the statistical analysis of a series of observations. In this case, the standard uncertainty is the experimental standard deviation of the measurement, which is derived from an averaging procedure or a regression analysis.
- Type B: The standard uncertainty is evaluated by a procedure other than the statistical analysis of a series of observations. In this case, the estimate of the standard uncertainty is based on other scientific knowledge.
All of them must be combined into what is called combined uncertainty, which is an estimate of the standard deviation equal to the root of the total variance obtained by combining all the uncertainty components.
After this combination, this uncertainty must be expanded, this is called expanded uncertainty: It provides the interval in which the value of the measurement will be found with a high level of confidence. It is obtained by multiplying the combined standard uncertainty by a coverage factor, said factor is based on the desired confidence level. For a 95% confidence level, k is 2.
What is the purpose of measurement uncertainty?
There are many advantages of taking measurement uncertainty into account. Estimating the uncertainty of the measurement allows us to have a more accurate knowledge of the state of the measuring instruments we use and the confidence in their measurements.
- Allows you to make decisions.
- Gives more meaning to the result of a measurement.
- Increases knowledge about the method used.
- Provides information about the results of a laboratory’s work. With this information, value and meaning is added to a laboratory result.
- Reliability and credibility are obtained and the processes are known in depth, which optimizes the procedures. No measurement is 100% accurate, so it protects against inaccuracy and false measurements.
- It represents scientific accuracy and reliability of the analyzed results.
- Provides a range of probable values in which the true value of a result can be found, confirming that no result has a unique value.
Key points of measurement uncertainty
There are several key points when determining, estimating and identifying the sources of uncertainty in a series of measurements.
To note:
- The instrument to calibrate: It is important to take into account, above all, the condition of the instrument that is going to be calibrated. A malfunction could cause high sources of uncertainty such as hysteresis and repeatability. In addition to this, in an analogue manometer one must know how to determine, according to DKD R6-1 regulations, the resolution of the manometer to avoid high sources of uncertainty.
- The standard with which it is going to be calibrated: The suitability of the standard selected for said calibration. The drift and uncertainty shed from the pattern can cause high expanded uncertainties. This can be anticipated by calculating the TUR, which should generally be 3:1, when selecting the pattern.
- Environmental conditions: Above all, temperature must be taken into account. Maintaining controlled environmental conditions can help us minimize uncertainty.
- Proficiency tests: Proficiency tests can help us know how we are in technical competence compared to other laboratories and the result of these to estimate an uncertainty that is as low as possible.
- Uncertainty is not an error: It is important to be clear about these concepts. If we confuse error with uncertainty we fall into the bad practice of treating uncertainty with error, that is, correcting readings with the value of said uncertainty. Uncertainty should not be added to the result to make reading corrections.
- The competence of the personnel: The technical competence and training of the personnel in charge of carrying out the measurements and then estimating the uncertainty is very important. When carrying out measurements, high repeatability and hysteresis may occur with personnel not suitable for such a task.
