Acceptance limits and the safety margin A

Why a reading near a limit needs care

GB/T 3177-2009 states the principle: the method of acceptance should accept only workpieces that lie within the limits of size. Every measurement has errors, so no measurement gives the true value. A general-purpose instrument usually measures size and not the form errors the workpiece may have, and the part is judged from a single measurement, with no corrections for temperature, contact deformation or systematic errors of the instrument and standards. A reading just inside a limit can therefore belong to a part that is just outside it.

The standard’s answer is acceptance limits, a permitted uncertainty for the instrument, and rules for choosing the instrument.

Acceptance limits and the safety margin

An acceptance limit is the size boundary used to decide whether a workpiece passes. GB/T 3177-2009 allows two ways to set it. In way a) the acceptance limits are moved into the tolerance zone from the maximum material size (MMS) and the least material size (LMS), each by a safety margin A; A is one tenth of the workpiece tolerance T. In way b) the acceptance limits equal the MMS and LMS, so A = 0.

For a hole the MMS is the lower limit of size; for a shaft it is the upper limit. Both formulas therefore pull both ends of the tolerance in by A.

When to use A and when A = 0

• Sizes under the envelope requirement and sizes of a fine tolerance grade: way a).
• When the process capability index C_p ≥ 1, way b) may be used; for a size under the envelope requirement, the MMS side still uses way a).
• For a size with a skewed distribution, way a) may be applied only on the side the sizes lean towards.
• Non-fitting sizes and sizes under a general tolerance: way b).

Reading Table 1: T, A and u1

GB/T 3177-2009 Table 1 lists, for tolerance grades IT6 to IT18 and sizes up to 500 mm, the tolerance T, the safety margin A and the permitted instrument uncertainty u1, in micrometres. Find the row for the size and the column for the grade. The cell used in the example below, IT9 over 18 to 30 mm, gives T = 52, A = 5.2 and u1 = 4.7, 7.8 and 12 µm for tiers I, II and III.

The tiers come from the ratio of the measurement uncertainty u to the tolerance: u is T/10, T/6 and T/4 in tiers I, II and III (grades IT12 to IT18 have tiers I and II only), and u1 is about 0.9u. Tier I is preferred, then II, then III. Unless stated otherwise, the uncertainties are for a 95 % confidence level, and the standard recommends the evaluation method of GB/T 18779.2.

Worked example: a Ø25 h9 shaft

GB/T 1800.2-2020 gives h9 at sizes over 18 to 30 mm as 0/−52 µm, so the limits are 24.948 and 25.000 mm. Table 1 gives T = 52 µm and A = 5.2 µm. For a shaft the MMS is 25.000 mm and the LMS 24.948 mm:

A reading of 24.996 mm lies within the limits of size but above the upper acceptance limit, so under way a) the shaft is not accepted. The instrument must have an uncertainty of at most 4.7 µm (tier I), 7.8 µm (tier II) or 12 µm (tier III).

Choosing the instrument with u1

Compare the instrument’s measurement uncertainty, from its calibration or your own evaluation, with u1. In NPL’s worked caliper example the expanded uncertainty is 0.035 mm (k = 2), a whole-measurement figure for a 0.02 mm caliper that includes repeatability; even so, it is about three times the widest tier, 12 µm, for Ø25 h9; a caliper measurement like that one does not meet GB/T 3177 for this shaft. See the caliper uncertainty budget and choosing an instrument for the tolerance.

How large are the risks?

Annex A of GB/T 3177-2009 (informative) calls accepting a part outside the limits a false acceptance and scrapping a good part a false rejection. With normally distributed sizes and measurement errors and A = 0, false acceptance is about 1 % and false rejection about 2 % at C_p = 0.67; at C_p = 1 they fall to about 0.08 % and 0.4 %. These are the standard’s round figures, close to tier II, with u = 2s.

The same annex shows how A relates to u: when C_p < 1, tier I uses A = u (the full uncertainty), tier II A = 3u/5 and tier III A = 2u/5. With u = T/10, T/6 and T/4, all three give A = T/10.

Safety margin and guard band

Way a) places the acceptance limits inside the tolerance, which JCGM 106 calls guarded acceptance. The difference is the size: GB/T 3177 fixes A at T/10 and limits the instrument through u1, while a guard band under JCGM 106 or ISO 14253-1 is taken from the expanded uncertainty U you evaluated (see decision rules and guard bands). Disputes are settled with a more accurate instrument or a method agreed beforehand; in general, conformity is decided according to GB/T 18779.1. GB/T 3177-2009 cites the 2002 edition of GB/T 18779.1; the current edition is GB/T 18779.1-2022.

Practising in KELIBRON

The lab judges by simple acceptance, which corresponds to way b): a value within the closed tolerance interval passes, using the corrected value before rounding. It gives no verdict when the tolerance band is narrower than two divisions (the resolution) of the gauge or when the value lies within half a division of a limit. No lab part has a safety margin yet, so acceptance limits are worked on paper.

In the practice scene a 0.01 mm digital caliper measures the depth of a blind bore drawn as 15 +0.05/0 mm. As a non-fitting size it takes way b), so the acceptance limits equal the limits of size; if way a) were applied, A = T/10 = 0.005 mm would give 15.005 and 15.045 mm. The bore is made 14.93 mm deep, below the lower limit of 15.000 mm, so it fails either way.