Measurement uncertainty in the evaluation
How uncertainty is computed and propagated in this tool — Type A evaluation of the mean, propagation to response and relative response, the coverage factor, and why the uncertainty is reported but not applied to the verdict.
Last reviewed
Every computed quantity in this tool carries an uncertainty. Understanding what it includes — and what it deliberately does not affect — is necessary to interpret a result correctly.
Type A evaluation of the mean
Type A evaluation of uncertainty is evaluation by statistical analysis of repeated observations, as distinct from Type B, which is evaluation by other means.
At each test point the standard uncertainty of the mean is:
The √n divisor is the reason the reading count matters. Doubling the number of readings does not halve the uncertainty of the mean; it reduces it by a factor of about 1,41. Going from 10 readings to 20 reduces it by 29 %, and from 20 to 40 by a further 29 %.
This is the same sample standard deviation used in the statistical fluctuation evaluation of IEC 60846-1, the worked example used throughout this site. The two use the same statistic for different purposes: fluctuation judges the scatter itself against a limit; uncertainty uses it to describe how well the mean is known.
Propagation
Response
Response is the mean divided by the reference value. Its relative uncertainty follows the mean:
Relative response
Relative response is a ratio of two responses, each with its own uncertainty. They combine in quadrature:
A consequence worth noting: the uncertainty of the reference point propagates into every other point. A reference measured with few readings raises the uncertainty of the entire dataset, no matter how carefully the other points were measured. Where reading counts must be limited, the reference point is the last place to economise.
Linearity-corrected rows
Where an energy response evaluation applies a linearity correction — in IEC 60846-1, the energy response test — the correction factor is itself derived from measured points and carries its own relative uncertainty. That component is combined into the result for those rows, so a corrected row has a larger uncertainty than an uncorrected one. The correction improves the accuracy of the value and reduces the confidence in it, and both effects are visible in the output.
Reporting
Uncertainty is reported as ± u to two significant figures, alongside the value it applies to. The value is displayed with one more significant figure than the entered data, so the uncertainty is not truncated by the display precision.
Exclusion from the verdict
The verdict compares the computed value against the acceptance limit directly. The uncertainty is not applied to that comparison.
This is deliberate and it is the single most important thing to understand about the output.
A relative response of 1,21 against an upper limit of 1,22 is recorded as a pass. If its uncertainty is ±0,04, the true value may well be above the limit. The tool does not make that judgement.
Basis for the exclusion
Applying uncertainty to a decision requires a decision rule — a stated policy on how the uncertainty is used, normally in the form of a guard band. That policy is not a property of the measurement. It depends on the consequence of an incorrect decision, on the conformity assessment framework in use, and on what the organisation has agreed with its assessor. Two laboratories evaluating the same instrument may legitimately apply different rules.
A tool that silently applied one rule would produce verdicts that appear authoritative and are not transferable between organisations. Reporting the value and the uncertainty separately leaves that decision where it belongs.
Practical application
Compare the margin against the uncertainty before accepting a marginal result. Where the margin is smaller than the uncertainty, the correct statement is that conformity cannot be demonstrated at that point — not that the point passed. See reading the results for how this appears in the output.
Components not included
The uncertainty computed here is the Type A component from the repeated readings, propagated through the calculation. It does not include:
- the expanded uncertainty of the conventional true value of the reference field, which is a property of the calibration laboratory and appears on its certificate;
- positioning uncertainty, field non-uniformity, or air density corrections;
- any Type B component for instrument resolution, drift, or environmental influence.
A complete uncertainty budget for a formal conformity assessment must include those components. The value reported here is one contribution to it, not the whole of it. The one place the tool does use the field’s expanded uncertainty is an acceptance rule stated relative to a set field value, as in the IEC 60846-1 alarm accuracy test, where it widens the exposure conditions rather than the verdict.