What was found
N530TM HAD AN UN-COMMANDED SHUTDOWN OF THE RIGHT HAND ENGINE INFLIGHT. THE RIGHT "NO DISPATCH" ANNUNCIATOR LIGHT HAD BEEN ILLUMINATED PRIOR TO THE PREVOUS 2 STARTS ON THE TRIP BUT WENT AWAY AFTER START WITH A PRESS OF THE FADEC RESET BUTTON.BOTH ENGINES WERE OPERATING NORMALLY ON THE CHANNEL B FADECS FOR TAXI,TAKEOFF,CLIMB AND INITIAL CRUISE. DURING A SYSTEM DISCUSSION AMONG THE CREW , THE PILOT PRESSED THE CHANNEL SWAP BUTTONS TO PLACE THE ENGINES BACK ON CHANNEL A WHILE IN CRUISE AT 40,000 FT. WHEN SELECTED TO THE A CHANNEL THE LEFT ENGINE CONTINUED TO RUN NORMALLY HOWEVER THE RIGHT ENGINE IMMEDIATLY SHUT DOWN . AN ATTEMPT TO RESTART THE ENGINE ON CHANNEL A WAS TWICE UNSUCESSFUL AS THE AIRCRAFT DECENDED TO 28,000FT . A THIRD ATTEMPT ON CHANEL B WAS SUCESSFUL AT 28,000FT AND AIRCRAFT CLIMBED BACK UP TO 40,000FT. AIRCRAFT CONTINUED TO DAL WITH NO MORE ISSUES.