Type A vs Type B uncertainty: the difference that matters

The GUM's Type A and Type B labels describe the method of evaluation, nothing else. A Type A component is one whose standard uncertainty was obtained by the statistical analysis of a series of observations. A Type B component is one obtained by any other means. Both are standard deviations by the time they enter the budget, and neither is more authoritative than the other.

The persistent misconception is that Type A is somehow better because it is measured while Type B is estimated. It is not. A manufacturer's calibration certificate for a reference standard is Type B, and it may be the best-characterised number in your budget.

Getting each into standard form

• Type A: take n readings, compute the sample standard deviation s, and divide by √n to get the standard deviation of the mean, which is what you report if the result is the mean. s = 0.126 °C over 10 readings gives 0.040 °C; the same s over 4 readings gives 0.063 °C.
• Type B from a certificate: divide the expanded uncertainty by its coverage factor. U = 0.030 °C at k = 2 gives 0.015 °C.
• Type B from a limit: divide the half-width by the divisor for the assumed distribution, usually √3 for a plain ±a specification.
• Type B already stated as a standard uncertainty: use it as it stands.

A budget with both

One Type A term and three Type B terms for a comparison calibration, combined by the law of propagation for uncorrelated inputs with the coverage factor taken from GUM Table G.2.

The combined standard uncertainty is 0.0443 °C. Because the Type A term carries 81.4 % of the variance and rests on only 9 degrees of freedom, the effective degrees of freedom come out at 13.6 and the coverage factor at 2.21 rather than 2, giving U = 0.098 °C. Had every component been Type B, k would have been exactly 2.

Where the distinction actually bites

Three places, and only three.

• Degrees of freedom, and therefore the coverage factor. This is the main one, and it is why the budget has to record how many readings a Type A term came from.
• Correlation. Repeated observations under the same conditions can share systematic effects that the repeatability figure does not see. Repeatability measures scatter, not bias.
• What you can do about it. A Type A term shrinks as √n, so more readings genuinely reduce it. A Type B limit does not shrink by measuring harder; it shrinks by getting a better instrument or a better certificate.

A common mistake in both directions

Double counting is the frequent one: including a manufacturer's accuracy specification as Type B alongside a Type A repeatability term, when the specification already encompassed the scatter the repeatability measured. Pick the evaluation that fits the situation rather than adding both for safety.

The opposite mistake is treating a single reading as if it had a repeatability of zero. If you measured once, you have no statistical information about scatter, and the honest move is a Type B estimate of it from previous history, clearly labelled as such.

The labels do not belong in the arithmetic. They belong in the documentation, so a reviewer can see which numbers came from your own observations and which were inherited from somewhere else.