They give you a success % chance. If you simply test it you will see, moon phase, birth sign, guardian, etc etc DO NOT effect meld chance. If you think it does its pure superstition/luck.

There are only 2 things that chance that %. HQ item can increase chance by up to 5%, and low value. The same 2 materia will ALWAYS give the same % chance. 2 tier 1 with the lowest value on any gear 41+ will always give 42.5% if the gear is +1 you get 47.5%