I can't understand why my computer just shuts off whene

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I can't understand why my computer just shuts off whenever I try to do something. This event isn't too common but it happens enough to annoy me. Everything just powers down. No blue screen or system warnings or whatever. Just nothing. It all just shuts off like it was just powered down.

An example of what I'm doing is that I'm running just Facerig on medium settings and Firefox and a crash happens. Though it's a few minutes later after opening FR.

I built my rig 5 years ago, and now everything, save for the mobo & proc and the 1TB Seagate HDD, have been replaced by new hardware.

I had this problem 2 years ago with the first PSU - it was a 500W.. something. It came with this case: http://a.pomf.cat/oteiwj.txt I swapped it out and I think I might have one or two of the sudden computer crashes, but didn't act on it. I don't remember. I do remember that playing BF3 would cause it to crash, and I had it on the lowest settings.

I asked some of my friends and one said that it's the mobo & proc since they haven't been swapped, and another says that it's the PSU failing.

TL;DR Is it the mobo & proc causing my sudden computer crashes or the PSU?