Measurement accuracy and repeatability
Talking about the quality of any measurement instrument, manufacturers often specify two parameters that may describe its quality: the accuracy and the repeatability. And this is the place where a common misconception may arise as to which of them should be considered ‘better’ and which can be neglected.
Both terms are defined in the 3rd (latest as of January 2022) edition of the International Vocabulary of Metrology published and maintained by the Joint Committee for Guides in Metrology.
Paragraph 2.13 defines measurement accuracy as “closeness of agreement between a measured quantity value and a true quantity value of a measurand”. Paragraph 2.21 defines measurement repeatability as “measurement precision under a set of repeatabilty conditions of measurement”. In other words, measurement accuracy is defined for each single measurement and is a measure of how close the results provided by a measurement system to the actual value being measured. Measurement repeatability is defined for a series of measurements and is a measure of how close the measurement results will be if conducted under the same conditions which include measurement procedure, measuring system, operating conditions, to the actual value being measured.
Both accuracy and repeatability may be poor due to an improper measurement procedure or bad manufacturing quality of the measurement system. To illustrate the difference, let’s consider a system that measures the position of a small object on a flat surface and provides its X and Y coordinates in some abstract units. Also for the sake of illustration we’ll take a threshold of 5 units with a measurement having accuracy below this level to be considered good and poor otherwise.
Given the exact location of the object is known and is 100 for both X and Y coordinates, if the measurement system has both good accuracy and repeatability, the results of 20 measurements may look like this:
In this case the largest difference between the true value and any single measurement does no exceed 5 units which is a fairly good result. This is an indication of a good measurement accuracy. At the same time, all the measurement results are close together and the largest difference between any two of them also does not exceed 5 units. This is an indication of a good measurement repeatability.
For the measurement system with good accuracy and poor repeatability, the results may look like this:
The largest difference between the true value and any single measurement still does not exceed 5 units, but the measurements are scattered all around the true value. The latter is an indication of a poor measurement repeatability.
For the measurement system with poor accuracy and good repeatability, the results may look like this:
In this case the difference between the true value and any single measurement are larger than in the previous cases and apparently exceeds 5 units which is an indication of the poor measurement accuracy. However, all the measurements are close together, meaning that the repeatability is good.
For the measurement system with both poor accuracy and repeatability, the results may look like this:
In this case the difference between the true value and any measurement is on the poor level. The measurements are also scattered all around, so the measurement repeatability is also poor in this case.
Obviously, the best case scenario is when both accuracy and repeatability of the measurements provided by a measurement system are good. The case when the accuracy is good and the repeatability is poor may still be acceptable for many industrial applications, but may also be an indication of flaws in either measurement procedure or the workmanship of the measurement system. The last case with both poor accuracy and repeatability is obviously the worst, meaning that the selected measurement system badly fits the intended purpose.
All four cases on a single picture:
List of sources:
1. VIM3: International Vocabulary of Metrology https://www.bipm.org/en/publications/guides/vim.html
2. Python script used to generate the graphs in this article https://github.com/leonidpospeev/measurement-accuracy-repeatability
