It's amazing how complicated a "simple" thing like diameter can get, when form error rears its ugly head.
As was mentioned earlier, ASME Y14.5M-1994 has something called Rule #1 (a.k.a. the envelope rule, a.k.a. perfect form at MMC) as the default for size tolerances like diameter. There are two requirements that have to be met. One is that the feature must fit through an imaginary boundary of MMC size. The other is that the "actual local sizes" must all be within the specified limits. For the pipe OD example, you would need a precision bore of diameter 80.15 mm, at least as long as the part, to verify the boundary requirement and a mic or calipers for the local size requirement.
The "best fit" size that the CMM gives you is based on a least squares fit algorithm. It's kind of an average diameter, that unfortunately doesn't match either of the two requirements! The Minimum Circumscribed Cylinder algorithm, if available, would be the one to use for the boundary requirement on an OD. For the local size requirement, you would have to take a series of opposed point measurements and verify that they are all within the proper range.
A consequence of Rule #1 is that there is an indirect form control. If the feature passes both the boundary requirement and the local size requirement, all of its form characteristics will be controlled to a value equal to the size tolerance. For the diameter tolerance of 80 +/- 0.15 mm, the size tolerance is 0.30 mm. So the circularity, cylindricity, surface element straightness, and derived median line straightness all get controlled to a worst case of 0.30 mm. So the size tolerance indirectly controls how much out of round or egg shape condition the feature can have. There can be an additional circularity tolerance to refine it further, but there doesn't have to be.
If one of the caliper measurements came out smaller than the lower size limit, the feature is nonconforming.
Evan Janeshewski
Axymetrix Quality Engineering Inc.