# Reproducibility

In metrology, the term “reproducibility” is the degree of agreement between a series of measurements of the same measurand (the quantity being measured), when the individual measurements are made by changing one or more conditions. For example:

• by changing the method of measurement;
• by substituting the operator for the measurement;
• Replacing the measuring instrument;
• moving to another location;
• changing the condition of use of the instrument or measurand;
• making measurements over longer or shorter periods of time.

Reproducibility is not to be confused with repeatability, which evaluates the agreement of measurement results by maintaining the same conditions, and carrying out the series of measurements in the short term. As with repeatability, the uncertainty is based on statistical measures. Manufacturer claims of instrument reproducibility must be based on multiple tests (replication) performed in different labs on a single unit or model of the instrument.

In some cases the concept of reproducibility overlaps with the metrological concept of stability. For example, when assessing reproducibility as room temperature changes (temperature stability) or over a long period of time (time stability).

The evaluation of reproducibility is particularly useful when a boundary condition is expected to have significant influence on the measurements. In such a case it is appropriate to carry out a series of measurements in which this condition is varied in a controlled manner. The comparative evaluation of repeatability and reproducibility allows you to know the impact of the specific boundary condition on the measurements you are making.

It is specified in terms of scale readings over a given period of time. For a statement about reproducibility to be meaningful, it is necessary to specify the conditions that have been varied.

## Reproducibility error

The presence of reproducibility discrepancies highlights the existence of systematic errors that affect measurement accuracy. Errors that occur when making reproducibility evaluations are called reproducibility errors, and they constitute an element in the evaluation of measurement uncertainty.

Commonly, this error is expressed as the maximum deviation detected in a significant set of measurements:

$E_{rep} = (V_{max}-V_{min})$

where:

• $$V_{max}$$ = maximum measured value
• $$V_{min}$$ = minimum measured value

According to a statistical approach, reproducibility is expressed quantitatively in terms of the dispersion of the measurement results. A careful analysis of the variance of the dispersion makes it possible to calculate the uncertainty contribution of the reproducibility error. In practice, since it is difficult to perform a large series of measurements (for a rigorous statistical variance evaluation), a simplified, but essentially correct, analysis is used, as it is the result of a conservative approach.

## Reproducibility of a measuring instrument

The reproducibility of a measuring instrument is the reproducibility found on a particular instrument when other boundary conditions are varied. The assessment of instrument reproducibility is made when a change in a boundary condition, is expected to induce systematic errors on instrument measurements.

Some of the most significant boundary conditions include:

• position and/or orientation of the instrument;
• environmental conditions (temperature, humidity, atmospheric pressure);
• sensor power supply;
• execution of measurements over long periods of time (i.e. drift of metrological characteristics over time).

For the calculation of the reproducibility error, the general indications apply.