SC QUALITY GUILDTUR, TAR and guard-band calculator
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Enter the tolerance, the calibration uncertainty and how often instruments like this one arrive in tolerance. Get the test uncertainty ratio, the acceptance limits for several guard-band methods, and the probability of a false accept and a false reject for each.
ON THE EXAM · CCT IV.A, IV.C, CQE IV.E · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
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TUR and TAR
The test uncertainty ratio compares the tolerance being checked with the uncertainty of the check. ANSI/NCSL Z540.3 defines it as the tolerance span divided by twice the expanded uncertainty of the calibration process at about 95% (k = 2): TUR = (upper limit − lower limit) / 2U. For a symmetric tolerance ±T that is T/U.
The older test accuracy ratio compares the tolerance with the accuracy specification of the reference standard alone. TAR is easier to work out but leaves out resolution, repeatability, the environment and the method, so it nearly always looks better than the TUR. The common 4:1 rule of thumb is a TUR requirement.
False accept and false reject
Every reading is off by some amount, so near a limit a calibration can get the answer wrong in two ways.
- False accept (PFA, consumer's risk, Type II): the instrument is really out of tolerance, but the reading falls inside the acceptance limits and it goes back into service.
- False reject (PFR, producer's risk, Type I): the instrument is really in tolerance, but the reading falls outside, and it is adjusted or rejected for nothing.
Both depend on the uncertainty and on how the instruments are spread: a population that is nearly always well inside tolerance gives few false accepts whatever the TUR. Here the true values are taken as normal, with the spread set by the in-tolerance probability (end-of-period reliability, EOPR) from your calibration history. The measurement errors are normal with standard deviation U/k. PFA and PFR are the double integrals over the regions where truth and decision disagree, worked out numerically. Z540.3 requires PFA of 2% or less, or, where PFA is not calculated, a TUR of at least 4:1.
Guard bands
A guard band moves the acceptance limit A inside the tolerance limit T, so a reading must be further from the limit to pass. It lowers PFA and raises PFR. The methods compared here:
- Simple acceptance: A = T. No guard band.
- Subtract U: A = T − U. Simple and strict; at low TUR it rejects many good instruments.
- RSS: A = √(T² − U²). A smaller guard band than subtracting U.
- Managed guard band (Dobbert): A = T − U·M, with M = 1.04 − e0.38 ln(TUR) − 0.54. It is designed to keep PFA at or below 2% whatever the in-tolerance probability, and needs no guard band above a TUR of about 4.6.
- Solve for a target: the widest acceptance limits that keep PFA at your target.
The trade-off chart shows the cost: every step inward buys a lower PFA with a higher PFR.
Where U comes from
U is the expanded uncertainty of the calibration at this test point, not of the instrument being calibrated. Build it from its sources with the measurement uncertainty budget.
On the exam
CCT IV.A lists guard-banding, PFR (Type I error), PFA (Type II error), TUR, TAR and percent of tolerance among the uncertainty terms to apply. IV.C covers combined and expanded uncertainty, coverage factors and the statement of conformity with its decision rule. CQE IV.E covers metrology, including measurement error and its sources. Expect to compute a TUR or TAR, apply a guard band, and say which way a guard band moves each risk.