Decision rules: simple acceptance, guard bands and ILAC G8
A customer sends a thermometer with a tolerance of ±0.5 °C. You measure an error of 0.40 °C with an expanded uncertainty of 0.16 °C. Does it conform? The measured value is inside the tolerance, but the true error could be up to 0.56 °C. The answer depends on the decision rule: the agreed rule that says how measurement uncertainty is taken into account when you state conformity.
What ISO/IEC 17025 requires
ISO/IEC 17025:2017 requires that, when a customer asks for a statement of conformity, the decision rule is clearly defined and, unless it is already part of the requested specification or standard, communicated to and agreed with the customer (clause 7.1.3), and that the report identifies the rule that was applied (clause 7.8.6). ILAC G8:09/2019, Guidelines on Decision Rules and Statements of Conformity, describes the common rules and how to report them. The choice of rule is a decision about risk, and it belongs to the laboratory and its customer.
The guard band idea
Every rule works with an acceptance limit that may differ from the tolerance limit by a guard band w:
- Simple acceptance (also called shared risk): w = 0. The item is accepted when the measured value is within the tolerance.
- Guarded acceptance: w > 0, often w = U. The item is accepted only if the measured value is inside the narrower acceptance zone. This protects the customer from accepting items that are actually out of tolerance.
- Guarded rejection: the guard band lies outside the tolerance. An item is rejected only when it is clearly out of tolerance. Used when a false rejection is the more expensive mistake.
What the risk looks like
With a normal distribution, the probability that the true value lies within the tolerance can be calculated from the measured value, the limits and the standard uncertainty. Two cases are worth remembering:
- With simple acceptance, a measured value exactly on the limit has only a 50 % probability of conformance. Items close to the limit are accepted with a high risk.
- With guarded acceptance and w = U at k = 2, a value on the acceptance limit lies 2 standard uncertainties from the tolerance limit. The probability that it is actually out of tolerance is about 2.3 % (for large νeff and one limit).
Worked example: thermometer, tolerance ±0.5 °C, U = 0.16 °C
The budget from the step-by-step guide gives uc = 0.080 °C and U = 0.16 °C (k = 2). With guarded acceptance (w = U), the acceptance zone is ±0.34 °C.
| Measured error | Statement (interval ± U) | Probability of conformance | Simple acceptance | Guarded acceptance, w = U |
|---|---|---|---|---|
| 0.30 °C | Pass | 99.4 % | Accept | Accept |
| 0.40 °C | Conditional pass | 89.4 % | Accept | Do not accept |
| 0.55 °C | Conditional fail | 26.6 % | Reject | Reject |
| 0.70 °C | Fail | 0.6 % | Reject | Reject |
The interesting row is 0.40 °C. Under simple acceptance the thermometer passes, although there is a roughly 1 in 10 chance that its true error is outside the tolerance. Under guarded acceptance it does not pass. Neither answer is "right". They reflect different agreements about who carries the risk.
The four statements
ILAC G8 describes non-binary statements that tell the customer more than a plain yes or no. Metroloom labels results by where the interval measured value ± U lies:
- Pass: the measured value and the whole interval are within the tolerance.
- Conditional pass: the measured value is within the tolerance, but the interval crosses a limit.
- Conditional fail: the measured value is outside the tolerance, but the interval reaches into it.
- Fail: the measured value and the whole interval are outside the tolerance.
The "conditional" statements are exactly the cases where the decision rule matters.
How to choose a rule
- What does a wrong acceptance cost? Safety-relevant or legal measurements usually justify guarded acceptance.
- How large is U compared to the tolerance? If U is small (a high test uncertainty ratio), the difference between the rules affects few items.
- Is there a requirement already? Some product standards, regulations and customer contracts define the rule. Follow it.
Who decides. A calculator can show the statement and the probability for the inputs and rule you give it. The rule itself, and the conformity decision, are agreed between the laboratory and its customer. In Metroloom you choose the rule and record your own decision.