One should always plan the attack before going into the field. If one is charged with improving a process, one would plan the attack, which would include the "after" sampling, along with the comparison to the "before" stuff.
That said, in this instance, based on the description of the product there are few parts made per day, them how about just adding the new data onto the old in a run chart of some sort. I assume that there was historical data that suggested the need for improvement, so take some "after" parts (seperate enough from the "before" parts - maybe a "purge" of the process) and add the sample data to a run chart of the prior data - Average and moving range, for example. If the large size is an indication of being able to run only a few per hour or day, then I think only a few could be necessary. The improvement (or lack thereof) should be obvious. IF there is an improvement, continue to run more parts, enough to see expected variation over some time, then calculate capability.
I think the first step is to determine if the change was a real improvement.
