Estimate the uncertainty of each input quantity that feeds in to the final result (Type A and Type B estimates). Express all uncertainties in similar terms (standard uncertainty u).

There are two ways to estimate the size of uncertainties from each source

Type  A – evaluation using statistics (usually from repeated readings)

Type B – evaluation using any other information, past experiences, calibration certificates, manufacturer’s specifications, from calculation, from published information and from common sense.

In most measurement situations uncertainty evaluations of both types are needed.

Calculating standard uncertainty for a Type A evaluation

Where n is the number of measurements in the set and s is the estimated standard deviation. The standard uncertainty of the mean has historically also been called the standard deviation of the mean, or the standard error of the mean.

 

Calculating standard uncertainty for a Type B evaluation

You might only be able to estimate the upper and lower limits of uncertainty. You may then have to assume the value is likely to fall anywhere in between. Ie. a regular or uniform distribution.

Calculating for a Type B rectangularly distributed uncertainty

a is the mid-point between the upper and lower limits (half width)

To combine uncertainties they must be given in the same units and at the same level of confidence. They need to be converted into standard uncertainties.

A standard uncertainty is a margin whose size can be thought of as ‘plus or minus one standard deviation’. The standard uncertainty tells us about the uncertainty of an average (not just about the spread of values).  

Converting uncertainties from one unit of measurement to another

Uncertainty contributions must be in the same units before they are combined. As the saying goes, you cannot ‘compare apples with pears’.

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Good practice online modules

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• Measurement uncertainty
• Introducing uncertainty
• Basics of uncertainty analysis