I think he is one of the first American gun makers to use fixtures and setup tools to make repeatable and interchangeable parts over and over again.
No, Whitney had absolutely nothing to do with "interchangeable parts". Eli developed "Batch Manufacturing" during his contract for 1798 U.S. Muskets. He was habitually late with deliveries and his products were not very well made
Interchangeable musket components were realized at Springfield Armory with the U.S. Model 1840 Flintlock Musket.
https://americanlongrifles.org/forum/index.php?topic=55358.0
Absolutely right although I suspect that he was on the right track striving for a degree of interchangeability the Whitney Armory never achieved during his lifetime. I also suspect that the Ordnance Department was tolerant of his late deliveries because they were working toward the same end and thought that Whitney's efforts were valuable. The Springfield Armory actually achieved that goal with the M1842 musket and it is reasonable to say that Springfield was the most advanced precision manufacturing concern in the world for a considerable time.* There was a virtual parade of foreign ordnance officers visiting the armory before the Civil War, buying American machines and hiring American mechanics to teach their own personnel how to operate them. This was even true of Enfield (the RSM) and the London Armoury Company which were probably the only other arms making entities to achieve true interchangeability before the Civil War.
I saw an Ames lock mortising machine, as supplied to Springfield, in the London Science Museum a few years ago. It had come from Enfield and was complete with its tooling attached to it. I didn't really look at the tooling but a British friend, David Williams, pointed out to me that it was for inletting Lee-Metford actions. That machine was still in regular use in 1902.
[edit]*Kent would know better than me but I'm not certain about the short-lived M1835 flint musket, immediately superseded by the M1842. Very few were issued and only a tiny number escaped conversion to percussion. I've only looked at 1 or 2 and only one of those was likely in original flint. Simeon North was also working on this problem and some of the parts of the North-made Hall carbines are effectively interchangeable albeit with tolerances that are fairly loose.