Decision Rules and Guard Banding in Calibration

Your micrometer reads 0.019 mm against a tolerance of 0 mm ± 0.02 mm, and the expanded uncertainty is 0.002 mm. Does it pass? There is no answer to that question until someone has agreed a decision rule, because on the numbers alone the true value could sit either side of the limit.

A decision rule is the agreed process for turning a measured value into a conformity decision. It is the thing most commonly missing from UK calibration and inspection records, and it is the reason "within tolerance" arguments happen after the fact rather than before. This guide covers what a decision rule is, the two ways they are built, and how guard bands actually get calculated.

The UK reference is UKAS LAB 48, Decision rules and statements of conformity, Edition 5, July 2024. It is free, and UKAS M3003 — the uncertainty document — explicitly hands this topic over to it.

This post assumes you already have an uncertainty figure. If you do not, the measurement uncertainty guide covers how to get one, and the Measurement Uncertainty Calculator will combine your contributions.

What a Decision Rule Is

LAB 48's definition is refreshingly short:

"A decision rule describes the agreed process for making a conformity decision. The rule explains how to use a measured value to decide whether a specification has been met and it explains the role of measurement uncertainty in reaching that decision."

Two words in there carry the weight. Agreed — the rule is settled between the parties in advance, not derived after an awkward result. And process — it is a method, not a number.

LAB 48 also separates the rule from the specification. Specifications "describe the desired characteristics of some quantity of interest (the measurand)" and "can be thought of as describing the requirement for the 'true' value of the quantity." They may be two-sided (a tolerance interval between an upper and lower limit) or single-sided (an upper limit only). The specification says what the true value must be. The decision rule says how you decide whether your measurement demonstrates that.

Why Uncertainty Changes the Answer

The reason a decision rule is needed at all is that you never measure the true value. LAB 48 puts it as: "A measured value therefore provides only an estimate of the 'true' value for the quantity of interest. The measurement uncertainty for the measured value characterises the likely range of values for the 'true' value."

Picture the tolerance interval as a window and your measurement as a probability distribution centred on the reading. When the reading sits comfortably in the middle, almost all of that distribution is inside the window and the call is easy. When the reading creeps toward a limit, part of the distribution falls outside — meaning some non-conforming true values could have produced the reading you got. LAB 48 describes this directly: for the same measured value, "if the measurement uncertainty is larger, then a larger proportion of nonconforming 'true' values … could have been responsible for the measured value."

Which leads to the sentence worth pinning above the bench:

"Clearly, if measurement uncertainty is not considered at any stage of a decision process the risk remains undefined (or uncontrolled) and the conformity decision is worthless."

That is the whole argument for decision rules in one line. A pass/fail stamp with no stated rule is not a conservative decision or an aggressive one. It is an undefined one.

The Two Kinds of Rule

LAB 48 states there are two common types: "those based upon simple acceptance criteria, and those based upon guard bands. In both cases, the rule defines a range for measured values that are considered to indicate conformance, this is known as the acceptance interval."

The difference is where uncertainty gets applied.

Simple acceptance — uncertainty as a pre-condition

Under simple acceptance, "sometimes called 'shared risk'", the rules "all equate the acceptance interval with the tolerance interval." Anything measured inside the limits passes. Uncertainty has not disappeared, though — it moves to the entry criteria: "Measurement uncertainty is taken into account by defining constraints that must be met before the simple acceptance decision can be made."

LAB 48 is explicit about the role this plays: uncertainty acts "as a pre-condition for the use of simple acceptance criteria."

The usual pre-condition for a two-sided specification is a minimum measurement capability index. LAB 48 gives it as:

C95 = (TU − TL) / (2 × U95%)

where TU and TL are the upper and lower tolerance limits, and U95% is the expanded uncertainty at 95% coverage. The higher the index, the sharper your measurement is relative to the tolerance you are judging against. LAB 48 adds that "in practice, various other parameters, and differing terminology such as Test Uncertainty Ratio (TUR), can also be used provided they contain the measurement uncertainty" — and warns that "to avoid any ambiguity when used, C95 should be defined along with the accompanying decision rule in contract agreements and in reports and certificates."

Its worked example of such a rule:

PASS: when measured temperature is between 18 °C and 22 °C, AND C95 ≥ 5 FAIL: otherwise

Alternatively the constraint can cap the uncertainty outright:

PASS: when measured value is below 2200 kg, AND expanded uncertainty U95% ≤ 100 kg FAIL: otherwise

Note what happens if the constraint fails. The rule does not quietly pass the item — the constraint was the thing making simple acceptance defensible, so a measurement too coarse to meet it cannot use this rule at all.

Guard bands — uncertainty in the boundary

Simple acceptance has a specific weakness, and LAB 48 quantifies it: under such a rule, values "up to and including the tolerance limits are taken to indicate conformance, with an associated risk of false decision of 50 % for values at the tolerance limit (and potentially higher risk for two-sided specifications)."

Fifty per cent. A reading sitting exactly on the limit is a coin toss. That is acceptable when the capability index is large, because then only a sliver of the allowed range is affected — but LAB 48 notes "there will be situations where this risk is too high."

The fix is to shrink the acceptance interval: "the acceptance interval can be reduced by an amount known as a guard band, so that the maximum risk of false acceptance is reduced to a desired level." Guard bands "can be applied to both single-sided and two-sided specifications."

How wide? LAB 48 gives the standard choice:

"Typically, guard bands are defined to have a width w equal to the 95 % coverage interval U95% w = U95% for which there is only a 2.5 % risk of false acceptance for both single-sided specifications and for two-sided specifications where C95 ≳ 1.5"

So the default guard band is simply your expanded uncertainty, and it takes the false-acceptance risk from 50% at the limit down to 2.5%.

Its two worked examples make the arithmetic concrete:

Two-sided. Specification: calibration error is to be 0 mm ± 0.02 mm. With U95% = 0.002 mm, the guard band w = 0.002 mm, giving an acceptance interval of 0 mm ± 0.018 mm. Pass when the measured value is inside that; fail otherwise.

Single-sided. Specification: maximum storage temperature for product is 4.0 °C. Pass "when measured value is no larger than (4.0 °C − U95%)."

Which answers the micrometer question at the top. Tolerance 0 ± 0.02 mm, uncertainty 0.002 mm, so under a standard guard-banded rule the acceptance interval is ± 0.018 mm — and a reading of 0.019 mm fails, despite being inside the tolerance. Under simple acceptance with an adequate capability index, the same reading passes. Same measurement, same instrument, different rule, opposite outcome. That is precisely why the rule has to be agreed up front.

Rules Do Not Have to Be Pass or Fail

Two-outcome rules are what LAB 48 calls "binary decisions … as only two possible outcomes are defined." But "both simple acceptance and guard banded decision rules can be written in terms of multiple different outcomes."

Its multi-state example, for a specification of pressure ≤ 120.0 kPa:

PASS: when measured pressure P ≤ 120.0 kPa, AND U95% ≤ 2.0 kPa FAIL: when measured pressure P > 130 kPa, AND U95% ≤ 2.0 kPa otherwise "Retest"

This shape is often more useful in practice than a binary rule. Marginal results and results whose uncertainty is too large both route to a retest instead of being forced into a call nobody trusts. If your process has ever produced a "well, technically it passed" conversation, a retest band is usually the missing piece.

LAB 48 also covers decisions for 'qualitative' tests — examinations producing a nominal property such as colour or shape, or a position on an ordinal scale such as Rockwell C — where "the strict VIM concept of measurement uncertainty does not readily apply." Uncertainty still has a role, but the treatment differs; Edition 5 added a new worked example (2d) for exactly this case.

"Just Ignore the Uncertainty" Is Not a Decision Rule

Every laboratory gets asked. LAB 48 devotes an appendix to it — Appendix D, titled The problem with allowing decision rules that do not take account of measurement uncertainty. Its opening is unusually pointed for a guidance document:

"Conformity statements under ISO/IEC 17025:2017 require a decision rule (3.7) that takes account of measurement uncertainty. Some might argue that it is possible to 'take account' by ignoring it, if that is what the customer requests; however, this seems to require a rather contradictory belief that you can be 'doing something' by 'not doing something' (is it possible to 'obey a red stop light' by 'not obeying a red stop light'?)"

The distinction that matters: a customer can agree to simple acceptance. That is a legitimate decision rule where the risk is shared knowingly, and LAB 48 documents it as one of the two main types. What cannot be done is issuing a conformity statement while pretending uncertainty is not in play. The introduction to LAB 48 also flags that the document ends "with an explanation of why simple acceptance criteria on their own cannot define a valid decision rule" — simple acceptance needs its constraint to be a rule at all.

Edition 5 added a note to its example 4 about claims that "uncertainty has already been taken into account" — worth knowing if a supplier tells you that without saying how.

What This Means on a Certificate You Receive

If you buy calibration rather than perform it, the practical takeaways are short.

• A statement of conformity should come with its decision rule. If a certificate says "PASS" against a specification but does not state the rule, you do not know whether a marginal result was guard-banded or passed on simple acceptance.
• Check whether the uncertainty is inside or outside the pass call. These give different answers near the limit, and near the limit is exactly where it matters.
• A result close to the tolerance limit deserves a second look even when stamped PASS, because a simple-acceptance pass at the limit is close to a coin toss.
• If you set specifications for a supplier, set the decision rule too. Otherwise you have delegated a risk decision without knowing it.

The calibration certificate guide covers what else a certificate should contain, and when a result comes back the wrong side of the line, the out-of-tolerance procedure covers what has to happen next.

The Short Version

• A decision rule is "the agreed process for making a conformity decision" — agreed in advance, and it must address uncertainty's role.
• Without uncertainty in the process, "the risk remains undefined (or uncontrolled) and the conformity decision is worthless."
• Simple acceptance: acceptance interval = tolerance interval; uncertainty is a pre-condition (capability index C95 = (TU − TL) / (2 × U95%), or a cap on U95%). Risk at the limit is 50%.
• Guard banding: acceptance interval is narrowed by w. The default w = U95%, cutting false-acceptance risk to 2.5% (single-sided, and two-sided where C95 ≳ 1.5).
• Worked example: tolerance 0 ± 0.02 mm with U95% = 0.002 mm → acceptance interval 0 ± 0.018 mm.
• Rules can be multi-state — PASS / FAIL / Retest is often more honest than forcing a binary call.
• You cannot "take account of" uncertainty by ignoring it. Simple acceptance is a legitimate choice; pretending is not.

How CalProof Fits

A decision rule is only useful if it is recorded against the decision it governed. The common failure is that the rule lives in a contract or a procedure while the pass/fail lives on a certificate, and nobody can later reconstruct which rule produced a given call.

CalProof stores the calibration result (in-tolerance or out-of-tolerance) and the certificate against each instrument's record, alongside an optional uncertainty field where you record the uncertainty stated on the certificate — for example the expanded uncertainty and coverage factor — so a conformity decision and the evidence behind it stay together. When a result lands near a tolerance limit, the history and the recorded uncertainty are both visible on the same record rather than in separate PDFs — which is what you need in front of you to decide whether a marginal pass should be treated as a pass.

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To see the shape of the output, the sample audit pack is ungated and downloads as a single PDF.

Sources

• UKAS LAB 48 Edition 5, July 2024 — Decision rules and statements of conformity
• JCGM 106:2012 — Evaluation of measurement data: The role of measurement uncertainty in conformity assessment
• UKAS M3003 Edition 6, March 2024 — The expression of uncertainty and confidence in measurement

This guide summarises UKAS LAB 48 Edition 5 (July 2024) as published, and applies to UK calibration and testing activities. Section, example and appendix references are to Edition 5. LAB 48 is UKAS guidance; ISO/IEC 17025 is the authoritative standard, and the characterisation of its conformity-statement requirement quoted above is LAB 48's own. The decision rule appropriate to your measurements depends on your tolerances, your uncertainties and your agreement with your customer. Verify against the current published edition and your UKAS assessor. This is not legal or compliance advice.