I have a Galaxy S7 that sometimes does not ring when called. I've tested it: it doesn't ring silently, doesn't vibrate, and there's no "missed called" indicator. The call goes straight to voicemail.
This post seems to have the answer:
...but that was for the Galaxy 2, and the menus must have changed. My phone doesn't have a
Settings > Call > Other Call Settings > Phone Settings
...path, nor a
Settings > Apps > Dialer > Show notifications