Tolerance versus uncertainty

A tolerance (or maximum permissible error) is a limit set by a specification or by the user. Measurement uncertainty is a property of the calibration result. They are compared, not confused: to state that an instrument is within a ±0.5 °C tolerance you need a measured error and an uncertainty small enough to make the statement meaningful.

The ratio

A common practice is to aim for a calibration uncertainty no larger than about a quarter to a third of the tolerance, so that conformity decisions are not dominated by uncertainty. Where that cannot be achieved, the decision rule must say how the risk is shared — guard banding is the usual answer.

On the certificate

ISO/IEC 17025 requires that a statement of conformity identifies the decision rule applied. Without it, 'pass' has no defined meaning.

The ratio, and what it is called

The comparison between the two has a name. The test uncertainty ratio (TUR) is the tolerance divided by the expanded uncertainty of the calibration; the older test accuracy ratio (TAR) compared the tolerance to the reference standard's accuracy instead, and is a weaker statement because it ignores everything else in the budget. A TUR of 4:1 has been the working target for decades, and it is not arbitrary: at 4:1 the uncertainty consumes a quarter of the tolerance, and simple acceptance carries a false-accept risk small enough that most people are willing to ignore it.

When you cannot reach 4:1

Tight-tolerance work often cannot. A ± 0.1 °C logger specification needs U ≤ 0.025 °C to hit 4:1, which is beyond a comparison calibration in a dry block and at the edge of what a stirred bath with a good reference will deliver. The answer is never to quietly quote a smaller uncertainty. It is to choose a decision rule that shares the remaining risk explicitly:

• Guard band the acceptance limits by U, or by a stated fraction of U, and say so on the certificate.
• Report non-binary results — pass, conditional pass, conditional fail, fail — so the customer sees where the interval sits relative to the limit.
• Widen the tolerance if the application genuinely allows it. A ± 0.1 °C specification copied from a datasheet is often tighter than the process needs.
• Improve the budget: a better reference, a better bath, more immersion, or more repeat readings. Look at the budget before assuming the answer is a more expensive standard — resolution is frequently the dominant term, and no reference thermometer fixes that.

Three words that are not interchangeable

Accuracy is a qualitative idea — how close a result is to the true value — and the GUM discourages using it as a number. Tolerance, or maximum permissible error (MPE), is a requirement: a limit you or a specification imposes on the instrument. Uncertainty is a property of a measurement result: the spread of values that could reasonably be attributed to the measurand. A specification sheet quoting accuracy: ± 0.5 °C is stating an MPE, whatever it calls it, and it is not an uncertainty.

The practical consequence: an instrument can be in tolerance and still be unfit, if the calibration that said so had an uncertainty comparable to the tolerance itself. Read the U on the certificate before reading the verdict.