I have the same problem on a new iPhone 6s. The problem did not happen with the previous phone. That said, I think it's the iOS 9.2 IMHO. The settings for do not disturb has a two selections for silence at the bottom of the screen for "always" and "only when the iPhone is locked". So when the phone is locked you can't receive a call and it goes to voicemail. I expect that's only supposed to happen when the phone is on "do not disturb", but it seems to be happening randomly anyway. The time of day is normally mid day eastern US time and it happened at least 3 times today, 31 Dec.
By the way I just tried resetting the network settings per the guidance above, and seems okay for now. I'll post again if it continues, and/or call the support line.
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