Test uncertainty ratio calculator (TUR and TAR)
Work out whether a laboratory's uncertainty is good enough for your tolerance, on the 4:1 basis ANSI/NCSL Z540.3 uses — and see why a healthy TAR can hide a failing TUR.
The item being calibrated
The calibration process
Take U and k from the calibration certificate. The standard’s tolerance is only needed if you also want the legacy TAR for comparison.
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Result
Below 4:1, Z540.3 does not forbid the calibration. It requires you to show that the probability of false acceptance is no more than 2 %, which in practice means guard banding the acceptance limits. Work that out in the guard band calculator.
Uncertainty at 95 % (k = 2)
0.3500 °C
To reach 4:1 you would need
U ≤ 0.2500 °C
At k = 2, for this tolerance.
Tolerance span
2.000 °C
±1.000 °C. TUR uses the full span, which is why an asymmetric tolerance still has a single ratio.
A ratio is not an acceptance decision. It tells you how much room the measurement leaves inside the tolerance; whether a particular result passes depends on where it falls and on the decision rule your quality system has agreed. ISO/IEC 17025 clause 7.8.6 requires that rule to be stated and applied, and ILAC-G8 describes the options.
How the calculation works
- 01TUR = tolerance span ÷ (2 × U₉₅), following ANSI/NCSL Z540.3 and its handbook. The full span is used, so an asymmetric tolerance still has a single ratio.
- 02The uncertainty you enter is re-expressed at k = 2 before the ratio is formed. TUR is defined on the 95% basis, so a figure quoted at k = 1 would otherwise flatter the result by a factor of two.
- 03Z540.3 clause 5.3(b): at or above 4:1 the measurement may be accepted without further analysis; below it, the probability of false acceptance must be shown to be no more than 2%.
- 04TAR, where a standard's tolerance is supplied, is tolerance span ÷ (2 × standard tolerance). It is reported for comparison only and never as the acceptance criterion.
Limitations
- A ratio is not an acceptance decision. Whether a particular result passes depends on where it falls relative to the limits and on the decision rule your quality system has agreed.
- Below 4:1 this tool stops and hands over to the guard band calculator rather than repeating the false-acceptance maths in a second place, where the two could drift apart.
- TUR is a US convention from Z540.3. ISO/IEC 17025 and ILAC-G8 frame the same problem as a decision rule and a statement of risk rather than as a ratio.
- It assumes the uncertainty you enter is the uncertainty of the whole calibration process, as the certificate reports it, not just that of the reference standard.
Frequently asked questions
- What is the difference between TUR and TAR?
- TAR compares the tolerance of the item with the tolerance or accuracy specification of the standard used. TUR compares it with the expanded uncertainty of the whole calibration process, which includes the method, the environment, repeatability and the item itself. A laboratory can show a comfortable TAR and a failing TUR at the same time, and that gap is exactly why ANSI/NCSL Z540.3 moved to TUR.
- Why does the coverage factor matter?
- TUR is defined against the expanded uncertainty at about 95%, which means k = 2. An uncertainty quoted at k = 1 is half the size of the same uncertainty quoted at k = 2, so using it directly would double the apparent TUR. This calculator converts whatever coverage factor you enter to the 95% basis before forming the ratio.
- Is a TUR below 4:1 a failure?
- Not in itself. Z540.3 allows acceptance without further analysis at or above 4:1; below that it requires you to show that the probability of false acceptance is no more than 2%, which in practice means guard banding the acceptance limits. A 3:1 ratio with a properly calculated guard band is compliant; a 3:1 ratio with no analysis is not.
- Does ISO/IEC 17025 require a 4:1 ratio?
- No. ISO/IEC 17025 clause 7.8.6 requires a documented decision rule and a statement of the risk taken, which is a more general requirement than a fixed ratio. The 4:1 convention comes from ANSI/NCSL Z540.3 and its predecessors, and is widely used in practice even where it is not formally required.
- Which tolerance do I use for an asymmetric specification?
- The full span, upper limit minus lower limit. TUR divides that span by twice the expanded uncertainty, so a +2 / −1 tolerance is treated as a span of 3 and has one ratio rather than two.
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What is a decision rule and why every certificate needs one
A decision rule states how measurement uncertainty is accounted for when declaring pass or fail against a tolerance. Simple acceptance, guard banding and non-binary statements are the common choices.
Guard banding explained with a worked example
A guard band narrows the acceptance zone by a multiple of the uncertainty so that a 'pass' has a controlled probability of being wrong. Here is the arithmetic.
Tolerance versus uncertainty
Tolerance is what you require of the instrument; uncertainty is how well the calibration could measure it. A conformity statement needs both.
How to choose a calibration laboratory
Check the accreditation scope for the exact quantity, range and uncertainty you need; then evaluate turnaround, certificate quality and how they handle out-of-tolerance findings.