Repeatability vs reproducibility

Ten readings taken in a row by one person with one thermometer describe repeatability. The same measurement made on different days, by different people, or with a different thermometer of the same type describes reproducibility. If the reproducibility spread is much larger than the repeatability spread, some influence — the operator, the environment, the instrument — is not under control.

In practice

• Use repeatability for the within-run Type A component of a calibration.
• Use reproducibility (intermediate precision) when the result will be used across days or operators — for example, a laboratory's routine calibration uncertainty.
• A large gap is a diagnostic: investigate before quoting the smaller number.

What changes between the two

The formal distinction is a list of conditions held constant. Repeatability conditions keep the same procedure, operator, instrument, location and conditions of use, over a short period. Reproducibility conditions change at least one of them. Between the two sits intermediate precision, which is what most laboratories actually measure and rarely name correctly.

The gap is the finding

The number that teaches you something is not either standard deviation but the difference between them. Ten consecutive readings with a standard deviation of 0.008 °C, and the same measurement repeated across four operators over a month with a standard deviation of 0.045 °C, say that something changes between runs that nobody has identified: setup technique, immersion depth as each person judges it, ambient drift through the day, how long each operator waits for stabilisation.

That hidden influence belongs in the budget one way or another. Either it is identified and evaluated as its own component, which is the better outcome because it can then be reduced, or the larger intermediate-precision figure is used in place of the repeatability figure, which is honest but leaves the cause unfixed.

Which one belongs in your budget

• Repeatability, for the within-run Type A component of a single calibration performed in one sitting by one person.
• Intermediate precision, for a laboratory's routine calibration uncertainty, where the result will be produced on different days by different authorised staff. This is the right choice far more often than it is made.
• Reproducibility, for method validation and for interlaboratory comparison work, where the question is whether the method travels.
• Whichever you use, record the number of observations. A standard deviation from four readings is itself very uncertain, and that is what effective degrees of freedom exists to account for.

Repeatability is also the cheapest competence-monitoring tool there is: the same artefact measured independently by two authorised people, with the difference compared against the claimed uncertainty. It catches a drifting technique long before an audit does.

How many readings

A standard deviation computed from a handful of readings is itself very uncertain, and the GUM handles that through effective degrees of freedom: with ν = n − 1, ten readings give ν = 9 and a coverage factor near 2.26 for 95 % rather than 2. Four readings give ν = 3 and k = 3.18, which is a 59 % wider interval than the k = 2 most certificates assume. Ten is the usual practical minimum, and the reason is arithmetic rather than habit.