The problem is, every incoming call is answered by 1 phone, becomes a "missed call" on the 14 others.
Missed call is a useless bit of information at the best of times.
If they are worried about missing calls, then they need a console operator to ensure all calls are answered.
They should otherwise have the call answered using a mailbox or ACD so messages can be played to keep them on the phone while they wait, and giving them options to leave a message, etc....