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I have the same problem. My phone (Galaxy Note 3, running Android 5.0) fails to either ring or vibrate when I call it. And the phone goes straight to voicemail. Strangely I can make calls from the phone no problem.
No, "Do not disturb" is not set.
In "sounds and notifications", my ringtone is set to maximum.
"Vibrate when ringing" is also set.