What was found
UPON LEVELING AT FL310 WITH CRUISE POWER SET AND AFTER CLOSING ENGINE, ANTI-ICE COMPRESSOR STALLS. NR 2 ENGINE EPR DROPPED FROM 1.8 TO 1.2,EGT STARTING TO CLIMB, NR 2 THROTTLE TO IDLE. SLOWLY RESTORED NR 2 POWER AND CYCLED ENGINE ANTI-ICE BACK TO OFF, COMPRESSOR STALLS RE-OCCURRED, NR 2 THROTTLE BACK TO IDLE, OBSERVED 3 HARD COMPRESSOR STALLS, SHUTDOWN ENGINE IAW QRH. REMOVED AND REPLACED NR 2 ENGINE.