When you're crafting a weapon, in this case the Celtic Tetra Cylinder, and it says 13% completion per attempt, how high can you rise that and through which means?

I know that being in a production party can raise it, but do certain titles, or the Patron Set affect it?

I'm just trying to roughly calculate how many more materials I'll need. At 13%, I'll need 8x materials but if I got it up to 20%/attempt, then I'd only need 5x. Which would be so much more affordable :D

Thanks in advance for replies, and I apologize if I didn't ask my question in the most efficient format. Words are hard.