RE: Tolerance in text

["Jonathan West" <jwest -at- mvps -dot- org>]

>
> Perhaps as important is implied tolerance. Any dimension has an
> implicit rounding tolerance. So, "25 mm" actually means
> "25 mm + 0.49 mm / - 0.50 mm" because any dimension in that range
> rounds to 25 mm to the nearest millimetre, which is the accuracy
> implied by omitting the first decimal place.

I disagree with this concept of implied tolerance. My disagreement comes
from my background as an author and/or editor of several thousand pages of
national and international standards, where the correct writing and
understanding of tolerances is important.

If a dimension is specified as "25 mm +/- 0.2 mm", then when you measure the
dimension with a device whose mesurement uncertainty is x mm (x may be a
very small value, but it is *always* greater than zero), then you can only
be certain that the dimension is within the required tolerance if the
measured value is in the range (24.8 + x) mm to (25.2 - x) mm. This is
because the actual value of the dimension may vary by up to x mm from the
measured value, and you have no way of knowing by how much and in what
direction within that range the measured value is out.

Similarly, can be certain that the dimension is out-of-tolerance if the
measured value is less than (24.8 - x) mm or greater than (25.2 + x) mm. If
the measured value is within the range (24.8 - x) to (24.8 + x) mm or
(25.2 - x) to (25.2 + x) mm, then all you can say is that it is not known
whether the actual value is within tolerance.

This has a further consequence. It is absolutely necessary for the stated
tolerance to be greater than the measurement uncertainty, and preferably
greater by an order of magnitude or better. If the measurement uncertainty
is greater than the tolerance, then no matter what the measured value is,
you have no means of demonstrating that the *actual* value lies within the
required tolerance.

Therefore, the limits of your tolerances should be stated exactly, and you
should not make any assumptions regarding rounding errors.

Regards
Jonathan West

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