Decision rules and guard bands

What is a decision rule?

JCGM 106 defines it as a documented rule that describes how measurement uncertainty will be accounted for when accepting or rejecting an item, given a specified requirement and the result of a measurement. The rule sets the acceptance limits: the range of measured values that leads to acceptance is the acceptance interval, and the interval between a tolerance limit and its acceptance limit is the guard band.

JCGM 106 describes producer and user agreeing on the rule, implicitly or explicitly. Agreeing on it before measuring avoids having to choose a rule after a reading has landed close to a limit. A rule with guard bands of w = U, for example, narrows a 0.05 mm tolerance to 0.04 mm when U = 0.005 mm.

Simple acceptance

Under simple acceptance, also called shared risk, an item is accepted when its measured value lies in the tolerance interval, and rejected otherwise. Producer and customer share the consequences of wrong decisions. JCGM 106 notes that such a rule usually comes with a requirement that the uncertainty is small enough, for example U ≤ U_max; in its legal-metrology example an instrument with a permitted error of ±E_max is accepted when the estimated error e satisfies |e| ≤ E_max and, in addition, U ≤ E_max/3.

The weak point is close to a limit. When the measured value lies very near a tolerance limit and the distribution is symmetric, about half of the possible true values lie on each side, so the chance of a wrong decision can be as large as 50 %.

Guarded acceptance: acceptance limits inside the tolerance

Guarded acceptance moves the acceptance limits inside the tolerance. For an upper limit, w = T_U − A_U > 0. A common choice is w = rU with r = 1, so the guard band equals the expanded uncertainty U = 2u. With a normal distribution, a measured value lying exactly on such an acceptance limit still has at most about a 2.3 % probability of belonging to a non-conforming part; further inside, the probability is lower.

A reading of 19.997 mm passes under simple acceptance and is not accepted under guarded acceptance, because it lies in the guard band. The value U = 0.005 mm is an assumed example; in practice it comes from your own uncertainty evaluation.

Guarded rejection: acceptance limits outside the tolerance

Guarded rejection puts the acceptance limit outside the tolerance (w < 0), so that a part is rejected only on clear evidence. JCGM 106 uses speed enforcement as its example: with a limit of 100 km/h, a radar with a relative standard uncertainty of 2 %, and a required 99.9 % probability that the limit was really exceeded, the threshold is 100 / (1 − 0.02 × 3.09) ≈ 107 km/h.

Who carries the risk?

JCGM 106 names two risks for a single decision. The specific consumer’s risk is the probability that an accepted item is in fact non-conforming. The specific producer’s risk is the probability that a rejected item is in fact conforming. Guarded acceptance lowers the consumer’s risk at the cost of rejecting more good parts; guarded rejection does the opposite. Simple acceptance splits the risk between both sides. Near a limit, under simple acceptance, either probability can reach about 50 %. JCGM 106 also defines global risks, taken over all the parts a process produces, which this article does not cover.

What does ISO 14253-1 use by default?

For proving conformity, ISO 14253-1 sets a default guarded acceptance rule. JCGM 106 (2012), citing the 1998 edition, describes it as reducing the tolerance on each side by w = U = 2u. NIST authors described in 2015 a proposal for the revision: a guard band equal to the 95th percentile of the error distribution, in most cases about 82.5 % of U. The current edition is ISO 14253-1:2017; check its text, or the rule your customer specifies, before you use a number.

How does this relate to the 10:1 and 4:1 rules?

JCGM 106 links them to the measurement capability index C_m = T / (4u) = T / (2U), where T is the width of the tolerance. It warns that ratio rules such as “10 to 1” or a 4:1 test uncertainty ratio are sometimes ambiguously defined; C_m ≥ 4, for instance, means u ≤ T/16. For the Ø20 0/−0.05 mm example, T = 0.05 mm and U = 0.005 mm give C_m = 0.05 / 0.010 = 5.

Decisions in KELIBRON

The lab judges by simple acceptance: a feature passes when its value lies within the closed tolerance interval, and the comparison uses the corrected value before it is rounded to the scale. Two cases get no verdict: a tolerance band narrower than two divisions (the resolution) of the gauge (“This gauge’s resolution is too coarse to judge this tolerance”), and a value within half a division of a limit (“Too close to a limit to decide”). An invalid measurement, such as a caliper tilted beyond the allowed angle, gets no verdict and never passes. The Ø20 0/−0.05 mm shaft in the practice scene was made 20.07 mm, so it fails clearly. The lab does not yet offer guard-band exercises.