Uncertainty of measurement: what it means for your reference blocks
Anyone involved in hardness testing will have seen the phrase ‘uncertainty of measurement’ on the certificates supplied with the calibration blocks that are used to check the accuracy of your test machine. Some may have even pondered on what that really means. Most of us grew up with tolerances: a dimension is either within tolerance or it isn’t, giving yes/no clarity.
Uncertainty of measurement is a different concept altogether, and it’s the means by which accuracy is defined in metrology — and hence in hardness testing.
A tolerance is a permissible range of variation. If a shaft is specified at 50mm ±0.1mm, it’s acceptable anywhere between 49.9mm and 50.1mm — a requirement telling you the minimum and maximum size. Uncertainty of measurement is not a requirement. It’s a statement about the measurement process: how well we truly know the value we’ve measured. It’s an acceptance that no measurement is perfect.
When a reference block leaves a UKAS-accredited laboratory certified at 250 HBW with an expanded uncertainty of, say, ±2.25 HBW, that figure is not a tolerance. It defines the range within which the true value almost certainly lies — and ‘almost certainly’ has a precise meaning here.
The internationally accepted convention is to quote expanded uncertainty at a coverage factor of k=2 , meaning that true value has a 95% chance of being within the stated range of 4.5 HBW (±2.25 HBW). The remaining 5% isn’t ‘swept under the carpet’; it’s the honest statistical reality of measurement. Understanding k=2 is essential to reading any Brinell calibration certificate correctly. Tolerance hasn’t actually disappeared it’s just a different thing, a different way of thinking about the measured characteristics of a material.
This matters in practice. If your tester reads 252 HBW on a block certified at 250 HBW, and your machine’s uncertainty is ±3 HBW, then 252 HBW is entirely consistent with a true value of 250 HBW — the difference is within what the process can reliably resolve. To declare the machine out of specification on that basis would be a conclusion the result simply does not support.
The standards address this directly. The indirect verification of a hardness machine — assessing its performance against independently calibrated reference blocks — is at least partially the process from which the machine’s measurement uncertainty is derived. The errors and repeatability established during that verification, and the resulting uncertainty figures, inform the interpretation (and correction) of all subsequent test results.
The key distinction, for those new to this concept, is that uncertainty of measurement is not a fudge. It’s a rigorous, quantified expression of confidence in a result.
