What is a decision rule and why every certificate needs one

A logger reads 0.08 °C high against a tolerance of ±0.10 °C, with U = 0.05 °C. Is it in tolerance? The interval 0.03–0.13 °C crosses the limit. A decision rule is the agreed answer to that question.

Common rules

• Simple acceptance (shared risk): pass if the measured value is within tolerance, uncertainty ignored. Probability of false accept at the limit is up to 50 %.
• Guard band with w = U: pass only if the value is within tolerance minus U. Probability of false accept ≤ about 2.3 %.
• Guard band with w = U/2 or another fraction: a negotiated intermediate.
• Non-binary: 'pass', 'conditional pass', 'conditional fail', 'fail' bands that state where the interval lies.

ILAC-G8 and JCGM 106 describe these rules and the risks they imply. The rule should be chosen for the consequence of a wrong decision, then written down before the measurement.

The same logger, under each rule

Take the case from the top of this page: measured error 0.08 °C, tolerance ± 0.10 °C, U = 0.05 °C at k = 2. The measurement interval is 0.03 °C to 0.13 °C, so part of it lies outside the tolerance. Here is what each rule declares, and what it costs.

Note that the measurement did not change. The instrument did not change. Only the agreement about who carries the risk changed — and that is exactly what a decision rule is.

Choosing one: three questions

• What happens if a bad instrument passes? If the answer is a recalled batch or a patient dose, guard band with w = U or wider. If it is a re-check next month, simple acceptance may be proportionate.
• What happens if a good instrument fails? Rejecting a perfectly serviceable reference standard has a cost too. Where false rejects are expensive and false accepts are not, w = U/2 or non-binary reporting is often the better trade.
• What is the TUR? At 10:1 the rules barely differ and the argument is academic. At 2:1 they give opposite answers on a large fraction of instruments, and the rule is the single most consequential line on the certificate.

Who decides, and when

ISO/IEC 17025 clause 7.1.3 puts the decision rule in the review of requests, tenders and contracts — that is, before the work, not after the numbers come back. If the customer specifies a rule, the laboratory applies it and records the agreement. If the customer does not, the laboratory selects one, communicates it and obtains agreement. Choosing the rule after seeing a borderline result is the one sequence that is not available, because it converts a risk policy into a way of getting the answer you wanted.

In a regulated user organisation the same logic applies internally. The rule belongs in the calibration procedure or the quality agreement with the supplier, decided once for a class of instruments, rather than argued case by case by whoever is holding the certificate.

Where it has to appear

On the certificate, next to the conformity statement, in words a reader can act on: for example, conformity assessed using a guard band of w = U with acceptance limits of ± 0.05 °C; U = 0.05 °C at k = 2, approximately 95 % coverage. A statement of pass with no rule beside it tells the reader nothing about what was actually tested, and is a nonconformity under clause 7.8.6.