metrology.conformance

The conformance rule of IEC TC 29: a deviation, its limits and its uncertainty.

The instrument standards IEC technical committee 29 has written since 2013 decide conformance the same way, and say so in the same sentence. IEC 60942:2017 (sound calibrators) prints it in 5.1.15, A.1.2 and B.1.3, IEC 61672-1:2013 (sound level meters) in 5.1.21, IEC 61672-3:2013 in 4.1 and IEC 61260-2 and -3:2016 (band filters) in their introductions: conformance to a performance specification is demonstrated when both of the following hold,

(a) the measured deviation from the design goal does not exceed the applicable acceptance limits, and (b) the actual expanded uncertainty of the measurement, for a coverage probability of 95 %, does not exceed the maximum-permitted uncertainty the standard prints for that test.

Two things set this rule apart from the older one, which ISO 8041-1:2017 still uses (13.1 and 14.1) and phonometry.vibration.verify_weighting implements: the uncertainty is not added to the deviation, and the limits are inclusive. Annex D of IEC 60942 (Figure D.1) shows where the first comes from: the tolerance limits are not stated, but lie outside the acceptance limits by a guard band equal to the maximum-permitted uncertainty “for a 95 % coverage interval”. The guard band is what keeps a laboratory whose uncertainty is no larger than that maximum from passing an instrument outside its tolerance, and it does so at that coverage, not with certainty: it lowers the risk of a false acceptance without removing it. The same annex settles the second in so many words: “a measured deviation equal to a limit of an acceptance interval demonstrates conformance to a specification, providing also that the uncertainty of the measurement from the laboratory performing a test does not exceed the specified maximum-permitted uncertainty”. The uncertainty criterion is inclusive too: example 7 of IEC 60942 Table E.1 has an actual uncertainty of 0,15 dB against a maximum of 0,15 dB and conforms.

With two criteria there are four outcomes, and the standards number them the same way (IEC 60942 E.2.2, IEC 61672-1 C.2.2):

1. deviation within the limits and uncertainty within the maximum: conformance;
2. deviation within the limits but uncertainty above the maximum: non-conformance, because the measurement cannot demonstrate anything;
3. deviation outside the limits with an acceptable uncertainty: non-conformance;
4. both criteria failed.

ConformanceVerification.outcome is that number and ConformanceVerification.reason the wording the “Reasons” column of Table E.1 and Table C.1 gives it, so the eighteen printed examples of the two tables are reproduced to the letter as well as to the verdict.

The limits may be symmetric, as IEC 60942 writes them (an acceptance limit on the absolute deviation), or asymmetric, as IEC 61672-1 writes most of its own (+1,0 dB; -1,2 dB in Table C.1). A symmetric limit is given as one number and an asymmetric pair as (lower, upper). One end of the pair may be open: the stop band of IEC 61260-1:2014 Table 1 prints a minimum relative attenuation and a maximum of $+\infty$ (“+70; +∞”), and that is an acceptance interval with no upper limit, given as (70.0, math.inf). An interval open at both ends bounds nothing and is refused.

A deviation that reaches a limit through floating-point arithmetic, such as a measured 0,2 dB plus a correction of 0,1 dB against a limit of 0,3 dB, sums to 0,300 000 000 000 000 04 and would be turned away by its last bit. Both comparisons therefore accept a value within one part in $10^9$ of its bound, which is nine orders of magnitude below any resolution these standards report a deviation at.

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ConformanceVerification(
    deviation: float,
    uncertainty: float,
    lower_limit: float,
    upper_limit: float,
    max_uncertainty: float,
    unit: str = 'dB',
)

One measured deviation judged by the conformance rule of IEC TC 29.

The verdict is derived from the fields rather than stored beside them, so a result cannot say it conforms over numbers that do not. All five numbers are in the one unit the specification is written in, which unit names for the figure.

Attributes

property

Criterion (a): the deviation lies inside the acceptance limits.

Both limits belong to the acceptance interval (IEC 60942:2017 Annex D).

property

The outcome number of IEC 60942:2017 E.2.2 and IEC 61672-1:2013 C.2.2.

1 conforms; 2 the uncertainty exceeds its maximum; 3 the deviation exceeds its limits; 4 both.

property

Whether the measurement demonstrates conformance: (a) AND (b).

A deviation inside its limits measured with too large an uncertainty does not pass. It is not a failure of the instrument; it is a measurement that “shall not be used to demonstrate conformance” (IEC 60942:2017 5.1.16), which outcome tells apart.

ConformanceVerification.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the deviation, its uncertainty and the limits, as Figure E.1 does.

The acceptance limits are the two horizontal lines, the measured deviation the marker (a diamond when it conforms, a cross when it does not), the actual uncertainty the error bar and the maximum-permitted one the shaded band behind it.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Parameters

property

Why the measurement does or does not conform, as Table E.1 words it.

property

How much of its acceptance limit the deviation uses, as a fraction.

Read on the side the deviation lies: a deviation of -0,6 dB against limits of +1,0 dB and -1,2 dB uses 0,5 of the lower one. Above 1 the deviation is outside the limits. A deviation on the far side of a limit of zero (a negative distortion against (0, 3)) has no finite share and reads as infinity. An open side is never used up: on it the share is zero while the deviation is inside the interval. A deviation outside the interval always reads above 1, on whichever side it leaves: its share of the limit it crosses when that is above 1, and infinity otherwise (a stop-band attenuation of 40 dB, or of -5 dB, against (70, +inf)).

property

The actual uncertainty over the maximum permitted. Above 1 it fails.

property

Criterion (b): the uncertainty does not exceed the maximum permitted.

verify_conformance(
    deviation: float,
    *,
    uncertainty: float,
    acceptance_limits: float | tuple[float, float],
    max_uncertainty: float,
    unit: str = 'dB',
) -> ConformanceVerification

Verify one measured deviation by the conformance rule of IEC TC 29.

Conformance to a performance specification is demonstrated when the measured deviation from the design goal does not exceed the acceptance limits AND the actual expanded uncertainty does not exceed the maximum-permitted uncertainty, both limits inclusive (IEC 60942:2017 5.1.15 and Annex D; IEC 61672-1:2013 5.1.21). The rule reproduces every verdict of IEC 60942:2017 Table E.1 and IEC 61672-1:2013 Table C.1.

It is the rule, not a standard: the limits and the maximum uncertainty are what the standard prints for the test at hand, read off its own tables. phonometry.metrology.verify_sound_calibrator does that for IEC 60942.

Parameters

Returns: The ConformanceVerification, whose passes is the verdict and whose outcome and reason say which of the four outcomes it is.

Raises