# Repeatability

Repeatability is the degree of agreement between a series of measurements of the same measurand, when the individual measurements are made while leaving the measurement conditions unchanged. It is a static characteristic of an instrument defined as the ability of an instrument to reproduce a group of measurements of the same measured quantity, made by the same observer, using the same instrument, under the same conditions. In particular, measurements must meet the following conditions:

• the same method of measurement must be maintained;
• they must be carried out by the same operator;
• they must be carried out with the same measuring instrument;
• they must be made at the same location;
• they must be made under the same conditions of use of the instrument and the measurand;
• they must be carried out over a short period of time.

Repeatability should not be confused with reproducibility, which evaluates the agreement of measurement results by varying one or more measurement conditions.

## Repeatability Error

Errors that show up when making repeatability evaluations are called repeatability errors, and they are an element in the evaluation of measurement uncertainty.

Repeatability error is actually the lower limit of the maximum accuracy that can be obtained from measurements. This is because, while systematic errors might be improvable (by control of boundary conditions, instrumental or methodological improvement), random errors by definition are not.

The sources of random errors are endless, to name a few examples:

• inherent instability of the measurand (background noise, Brownian motion);
• reading errors by the operator
• disturbances on electrical circuits;
• local gravitational acceleration value;
• elastic deformation of support structures or equipment;
• instability of environmental conditions (atmospheric convection, infrared radiation);
• own repeatability of measuring instruments (instrumental repeatability errors).

The presence of discrepancies under the same measurement conditions indicates the existence of random sources of error. These are a natural effect of the practical impossibility of perfectly controlling all the infinite sources of influence. What is crucial in practice is that the discrepancies are not so large as to make the measurement non-significant. The assessment of repeatability is therefore fundamental in defining the accuracy of the measurement.

Specific claims of repeatability are based on multiple calibration tests (replication) performed within a given lab on the particular unit. The instrument repeatability reflects only the variations found under controlled calibration conditions.

## Repeatability of a measuring instrument

The repeatability of an instrument is the degree of agreement that is found on the measurements of a particular instrument, when measuring the same measurand, under the same conditions of measurement. Instruments, by their nature constructively complex, assume an infinite number of small errors of different nature, which combined result in random measurement errors.

The evaluation of the instrumental repeatability is part of the calibration of the instrument, and must be performed in laboratories that ensure the best control of the measuring conditions. In these laboratories, the measurement uncertainty has been evaluated, and this allows a correct assessment of the extent to which the instrument under test is repeatable.

It should be pointed out that in order to perform the repeatability of an instrument it is only necessary that the measurements are carried out: a) using a reference sample whose peculiar characteristic is the stability of the quantity supplied even in relatively short times but sufficient to perform the measurements, b) in an environment whose climatic conditions (especially temperature) are kept stable throughout the duration of the tests. Therefore, it is not necessary for the tests to be carried out by a specialized or certified laboratory since the outcome of the measurements does not depend on the uncertainty of the laboratory but only on compliance with the two points mentioned above. Generally, 25-50 repetitions of the measurement are performed and the standard deviation, or standard deviation, is calculated, which multiplied by a coefficient K, called coverage factor, establishes the probability that the true value of the measurand is included in the confidence interval of about 68.3% for K = 1, 95.45% for K = 2 and 99.73% for K = 3. Only in particular cases, like in automotive, it comes used the value K equal to 4 for a confidence interval of ≈ 99,994 %.

## Repeatability of an actuator

The repeatability of an actuator, where an actuator is defined as a mechanical organ that is positioned in space, is the ability of actuation and control systems to move to the same point in space as a result of other movements. For example, a robotic arm might repeat a path needed to accomplish a task and need to be located with some precision at specific points along the path.

Repeatability is affected by the speed at which the actuator moves, the time required to correct the final position, mechanical wear, and environmental conditions (temperature, humidity).

Sometimes the actuator is also required to correct for the effects of gravity on the actuator and possibly load inertia. For example, a piston pushing packages for packaging might be less repeatable if, from time to time, the packages are of different weights and contribute to the inertia of the piston’s motion.