Starting in the late 1200s there are some very significant advances in armor technology (coat of plates), but also evidence of what must have been an absolutely massive industry:

As an example in 1295 Frederic the Lombard assembled for the fleet of Philip the Fair in Bruges 2,853 helmets, 6,309 round shields, 4,511 mail shirts, 751 pairs of gauntlets, 1,374 gorgets and 5,067 coats of plates.7 Even with conservative estimates, this equals thousands and thousands of hours in labor and would need an impressive “industrial complex” to produce and deliver such a large order in a efficient way.

Another example is the armor store of Francesco Datini who imported armor to France from Milan. An inventory in 1367 showed 45 bascinets, 3 chape de fer (iron hats), 10 cervelles, 60 breastplates, 20 cuirasses, and 12 mail shirts in stock.7 If this equates to any type of average for an armor seller to have in house, we are contemplating a huge production capacity for the industry of armor making and one that points to wide spread sources of production, not just a few great centers which supplied the entire need for armor.

This continues into the 1300s:

The merchants would also check all product for quality before allowing the Nuremberg mark to be placed on it and allowing export and sale of the item.6 Such tight control sometimes limited the amount that could be made, as in 1362-3 when an order from Emperor Charles IV strained the resources to complete 1,816 armors.

And into the 1400s:

In preparation for the Battle of Maclodio, 1427, Milan was able to supply 4000 armors for cavalry and 2000 for infantry within just a few days.7

http://oakeshott.org/some-aspects-of-the-metallurgy-and-production-of-european-armor/

In the mid 1300s we start to see the coat of plates replaced by the breastplate, and after that point no other part of the world is able to match European armor technology. So what happened that allowed this massive growth in arms technology/production, and why didn't the rest of the world catch up?