I've experienced a few kernel page fault (fatal trap 12) on my FreeBSD 10.3-RELEASE server. They occur anywhere from milliseconds of uptime to days of uptime. The current process is always different (pagedaemon, pkg, find).
After reading online, the answer seems to point towards failing hardware. My question is how exactly does the failing hardware manifest itself in a kernel level page fault? Why doesn't failing hardware result in a Kernel panic with more descriptive information?
UPDATE: As per Bob's post below, I performed hardware testing. I had a bad RAM stick. I used memtest to determine that.