In my opinion, the DevOps culture come along with a methodology change toward Agile process management.
ITIL is heavily aimed at a clear formalism of the process and the results and thus more adapted to a Waterfall model.
This doesn't mean ITIL is incompatible with Devops, but usually this will be two separate process with different timelines.
I mean that ...
I'm ITIL certified (though it has been a while.) I agree with Tensibai: ITIL and DevOps aren't incompatbile, but that doesn't necessarily make them great friends.
The argument can be made that the processes in ITIL must happen in some way, especially for larger organizations. Successful integration of DevOps practices, where ITIL is already practiced, ...
Yes, DMAIC makes sense. If processes like CD need to be improved it is important to have a baseline. Therefore the Measure step is useful. The team investigates the status of process X, e.g. CD by documenting the current status.