Both when I was doing QA inspection and now that we contract for QA/NDE inspection we charged and were charged by the hour plus expenses.
The main reason for this is that the QA/NDE inspector has no direct control over the testing, at least as far as witnessing goes. He or she is just an observer who is verifying that what is reported on the WPQR is what actually happened. Very often, tests don't go as expected and more time is needed. (I've been on a 1 week job that ran for 2 months because fillet weld Tee tests wouldn't pass, the AWMT specimen was got lost, RT wouldn't pass, etc. They eventually got it together but I sure am glad that wasn't a flat rate.)
Not sure how others do it, that's just what I have seen. Hope it helps.
CHGuilford