Nope, no explanation available without watching over your shoulder.
I run a MacPro cylinder so anything I can tell you about my operation is pretty much useless but since you have called me a rocket scientist that qualifies me to make a few suggestions. Diagnosing seemingly random or baseless crashes is not easy these days. Used to be we'd run some binary tests and try to find a likely cause. The usual culprits are conflicting software (not likely these days), bad or corrupted third party filters and plugins (binary tests still work, disable half, disable the other half, etc), or bad media associated with a project (binary can help there too just tedious).
Well, we don't have EVERY detail about your system. You left out one of the most important items. We need to know the PRECISE version of AE you're running, rught down to the very last decimal point.
"AE CC 2015" is just too vague for a diagnosis.
Have you updated your AE to version 13.5.1?
What sort of things do you have in your comps when AE crashes?
What are you doing when it crashes?
What third-party plugins do you have installed?
Are you using the deprecated ray-traced renderer or are your comps set to use the standard renderer?
When AE crashes, does it give any error messages, if so, what do they say? When it crashes, what does it do? Does it blue screen? Does it lock up first and then crash? Does the screen flicker? Or does it just go BAM to your desktop without much fanfare?
Crash logs would be handy for the extremely techy folks, like Mylenium, I'm sure, but I'm more interested in the circumstances surrounding the crash.
I'm running Windows 7 with Service Pack 1 like you are, but on a lower-end system and I haven't experienced any crashes like you've mentioned. So, in order for us forum folk to narrow it down, we're going to need a lot more information.