Test uncertainty ratio (TUR) calculator
Enter the tolerance of the instrument under test and the expanded uncertainty of your measurement. The calculator gives the ratio, checks it against your target and works out guard-banded acceptance limits.
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Tolerance and uncertainty
Use the same unit for every value.
The tolerance of the instrument under test.
95 % coverage, k = 2. Work it out
4 means 4:1.
Optional. Shown beside the results.
Result
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Next: Calibration certificate
The uncertainty and the ratio are added to the certificate with your readings.
The TUR formula
TUR = (upper tolerance limit − lower tolerance limit) ÷ (2 × U), where U is the expanded uncertainty of your measurement at about 95 % coverage (k = 2). This is the definition in ANSI/NCSL Z540.3. For a symmetric tolerance of ±T it reduces to T ÷ U.
Example: a gauge with a tolerance of ±0.5 psi, calibrated with an expanded uncertainty of ±0.1 psi, has a TUR of (0.5 − (−0.5)) ÷ (2 × 0.1) = 5:1.
What goes into the expanded uncertainty
U is more than the accuracy of your reference standard. A complete figure combines every contributor that matters for the measurement:
- the uncertainty on the reference standard's own calibration certificate, and its drift since then
- the resolution of the standard and of the instrument under test
- repeatability, from repeated readings
- environment and setup effects, such as temperature, head height or lead resistance
The contributors are combined as standard uncertainties (root sum of squares) and multiplied by the coverage factor k = 2. Using only the standard's accuracy gives a test accuracy ratio, which looks better than the real TUR.
Guard-banded acceptance limits
When the ratio is below your target you can still make a sound pass or fail decision by tightening the acceptance limits. This calculator uses the guard band from ILAC-G8: the limit is moved in by U on each side. A reading inside the guarded limits is in tolerance with a risk of false acceptance below 2.5 %. Readings between the guarded limit and the tolerance limit are neither a clear pass nor a clear fail, which is why the rule has to be agreed with the customer first.
Questions
- What is a test uncertainty ratio?
- It compares how wide the tolerance is with how well you can measure. ANSI/NCSL Z540.3 defines it as the span of the tolerance divided by twice the 95 % expanded uncertainty of the measurement process: TUR = (upper limit − lower limit) ÷ (2 × U). For a symmetric tolerance of ±T this is simply T ÷ U.
- Why is 4:1 the usual target?
- At 4:1 the measurement uncertainty takes up a quarter of the tolerance, so the chance of passing an instrument that is really out of tolerance is small. ANSI/NCSL Z540.3 asks for a probability of false acceptance of 2 % or less and accepts a TUR of at least 4:1 where that probability cannot practically be estimated.
- What is the difference between TUR and TAR?
- A test accuracy ratio (TAR) compares the tolerance with the accuracy specification of the reference standard alone. A test uncertainty ratio uses the whole expanded uncertainty of the measurement: the standard, resolution, repeatability, environment and anything else that contributes. TUR is the stricter figure and the one current standards refer to.
- What can I do when the ratio is below 4:1?
- Use a better reference standard, reduce the other uncertainty contributors, or apply a guard band. With guarded acceptance the acceptance limit is the tolerance reduced by the expanded uncertainty (w = U in ILAC-G8), which keeps the risk of a false acceptance under 2.5 % whatever the ratio is. Agree the decision rule with your customer before you use it.
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Doing this for every instrument, every month?
Probatus stores the uncertainty with each reference standard and applies your decision rule on every calibration, so the check on this page happens without anyone doing the sum.