Your not the only one with this issue and while I can't help you as I am suffering from the same issue at least you can know your not alone and its unlikely your hardware. Much of the time it seems attributed to DX11 or else graphic driver crashes which effect DX9 as well with FFXIV:ARR. The common denominator seems to be from what I have seen those with OC graphics cards (usually factory OC ones).

For me I get this issue as well which most often happens when in a duty be it a trial, dungeon, and such but can happen other times. When run DX11 it seems more common. At times I can go days without a single crash playing most of the entire day even and other times will crash 5 times in one day. Computer just goes black, have some wierd static noise, and only way to fix is a hard restart. Crash logs either point to DX11 or the driver if its DX9 and it could happen on an ATI or a NVidia card.

My setup is a i4790 and a GeForce 970OC and all my parts are high end.