Test uncertainty ratio (TUR): what 4:1 really means
The test uncertainty ratio compares the width of a tolerance with the uncertainty of the measurement used to check it. It answers a simple question: is my measurement good enough for this tolerance?
How to calculate TUR
The usual definition divides the tolerance span by twice the expanded uncertainty at about 95 % coverage:
For a symmetric tolerance ±T this is simply T / U. In the thermometer example from the other guides, the tolerance is ±0.5 °C and U = 0.16 °C:
U here is the uncertainty of the whole calibration process, from the full budget: reference standard, environment, resolution, repeatability. It is not just the accuracy of the reference.
TUR is not TAR
The older test accuracy ratio (TAR) compared the specified accuracy of the device under test with the specified accuracy of the reference standard. It ignores everything else in the budget. A 10 : 1 TAR can hide a TUR of 3 : 1 once bath gradients, resolution and repeatability are counted. When someone quotes a ratio, ask which one it is.
Where 4 : 1 comes from
A ratio of 4 : 1 became the common rule of thumb in calibration, carried by military and industry standards for decades. It was a practical way to keep the risk of wrong decisions low without calculating it. ANSI/NCSL Z540.3 (2006) moved the focus to the risk itself: it requires the probability of false acceptance to be no more than 2 %, and only where estimating that probability is not practicable does it fall back to a TUR of at least 4 : 1.
Why a high TUR does not make every result safe
A high TUR keeps the average risk across many items low. It says nothing about an individual result close to the limit. A value measured exactly on the tolerance limit has a 50 % probability of being out of tolerance, whatever the TUR. What TUR changes is how wide the risky zone near the limits is.
With guarded acceptance and w = U, the acceptance zone is the tolerance minus U on each side. Its width as a share of the tolerance follows directly from TUR:
| TUR | U as share of T | Acceptance zone with w = U |
|---|---|---|
| 10 : 1 | 10 % | 90 % of the tolerance |
| 4 : 1 | 25 % | 75 % |
| 3 : 1 | 33 % | 67 % |
| 2 : 1 | 50 % | 50 % |
| 1 : 1 | 100 % | 0 %: nothing can be accepted |
At 4 : 1, a quarter of each half of the tolerance is a zone where the result is conditional. At 2 : 1, half of it is. That is the practical meaning of a low TUR: many results end up as conditional pass or conditional fail, and the decision rule decides their fate (see decision rules and guard bands).
What to do when TUR is low
- Look at the budget, not just the reference. The share column of the budget shows which source dominates. Often it is the environment or the fixture, not the standard (see the budget guide).
- Reduce the largest contribution: a better reference, a more stable bath, more readings to lower the Type A part.
- Agree a decision rule with the customer that matches the risk they can accept, and report it.
- Report the measured value and U instead of a pass/fail statement, and let the user of the instrument apply their own criteria.
In the Metroloom calculator, TUR is shown with every conformity check, next to the probability of conformance for the measured value. The first tells you how good the measurement is for this tolerance; the second tells you about this particular result.