Linux causes computer to randomly hard reboot, Windows doesn't

[tinybob20]

Hi,
I'm currently running Ubuntu 18.04 on my desktop, which I've been dual booting Linux/Windows on for the past couple of years. Recently, my computer has completely powered off (fans stop, everything loses power) and then immediately powered back on while I'm using it, usually between 5-30 minutes after I turn it on. Nothing has changed in the applications I've been running (usually just Chrome + Emacs). I originally thought it was my power supply, but just to test, I booted Windows to see if it would happen. Weirdly enough, I was able to keep Windows running for over 12 hours, and I was even able to stress test it for an hour (100% CPU + GPU) with nothing happening. While running the stress test, I didn't see anything get too warm either (I think max 50C on the CPU).
My hardware is:
i5 4670
MSI Z87-G41
MSI GTX 770

 

[tinybob20]

Update:
I ran memtest86+, and I found that 2 of my 4 sticks had 700+ errors, so I removed them. I'm still getting the reboot errors though. My computer has started rebooting in windows too, so I believe it's a hardware issue. I tested the voltages of the motherboard with a voltmeter while running a CPU stress test, and I'm getting a steady 12.2V, so I currently don't think there's something wrong with the PSU.