Security update 2016-003 10.11.6 issues
(I would add this as a comment, not an answer, but the system won't let me comment.)

I installed Security update 2016-003 on my iMac running OS 10.11.6 (El Capitan) on Dec 13. Since then I have had two kernel panics, one on trying to wake the computer and one today on startup.

The panic on startup occurred with the Apple logo and progress bar still on screen. There was a single line of text at upper left of the screen announcing the panic. No panic report in logs for that one.

Apple diagnostic test says there are no hardware problems, so I strongly suspect the security update is causing these panics.

Update Dec 21: In my case the kernel panics stopped occurring after I updated Little Snitch from 3.6.4 to 3.7.1. Compatibility with Sierra was added at v3.7.0. Perhaps that also provides compatibility with the El Capitan security update 2016-003. Or perhaps it was just the Little Snitch reinstall process that fixed things.