unexpected system shutdown while being used

For the last 2/3 months I have sometimes noticed (but never seen first hand) that if I left my computer on for a few hours that sometimes Id come back and it had turned itself off, and then of course when I went to turn it back on the "Windows has been shut down illegally start in safe mode etc" message came up.

However I ignored it as it wasnt as yet directly effecting me using my PC. Unfortunately 3/4 days ago it shut down whilst I was using it and it has since been a pretty regular occurrence.
There doesn't seem to be a definite pattern to the shut down,
It has shut down while I was watching a video, as well as on the internet with many tabs on and music playing. Also it does it if I initiate a virus scan and most interestingly if I run a memory diagnostic it shuts down.
This led me to think it might be a hardware issue, the problem being that
it has never shut down during safe mode and I left it on the BIOS screen for several hours with no shut down. Also I can initiate a virus scan in safe mode and it wont crash.
Ive already performed a system restore.Any ideas? Tanx a lot the minidump data says 122115-2168-01.dmp as at 12/12/2015

thanks a lot in advance guys