The low frequency noise can vary quite a lot from one sample to another. Its also rather slow an thus expensive to measure. Even with expensive parts like the LTZ1000, there are good ones an bad ones with way more LF noise than typical specs. So it really makes sense to have a system for LF noise measurements.
True but the LTZ1000s are *very* expensive and given that noise is a very important characteristic, a close second to stability, then I don't think it is unreasonable that they should be 100% tested for noise. And since LT specify a maximum of 2uVpp, 1.2uV typical it looks like they have the same opinion. Of course you could still get parts exceeding the maximum but according to TI:
"All data sheet specs are usually obtained using a +/-3 sigma truncation of a typically Gaussian distribution of parts over process variations".If your application demands parts that are more tightly specced than the datasheet maximum, or 3-sigma probability is not adequate of course you will need to test each part.
The LTC6655 are a lot cheaper, but still relatively expensive, so given the major headline feature is its very low noise, I don't think it would be unreasonable for some sort of noise screening to be performed - even if it were a very quick, and hence cheap, test for HF noise and LF noise at say 10Hz. LT on the other hand (like the vast majority of voltage references from all manufacturers) don't even bother to specify a maximum so in this case they don't agree. One would hope that in reality that the manufacturing process is well enough controlled, along with periodic QA testing, to ensure that the majority of parts do not exceed a reasonable multiple of the typical figure. The problem is what is reasonable? Given Andreas's noise measurements so far I personally would be a bit wary of the LTC6655 - but it is a very small sample.
Besides electronic LF noise, there can also be thermal noise from turbulant air flow and thermal EMF and similar. This can look rather similar to 1/f noise.
True, but Andreas's results for various other references have been roughly in line with the datasheet specifications which suggest that his procedures and test setup are good enough and have the above issues under control. It is just the 6655 results which are unexpected hence the question as to whether they have a particular problem in his setup such as inadequate decoupling, instability/HF oscillations etc.