What was found
CREW REPORTED ENGINE FLAMEOUT AT FL346 AND REQUESTED DESCENT TO FL290. CREW DECLARED AN EMERGENCY AND WERE VECTORED. CREW RAN ENGINE FAILURE AND RELIGHT CHECKLIST. ENGINE RELIGHT WAS SUCCESSFUL AT FL280. ACFT CONTINUED AND USING NORMAL PROCEDURES, LANDED UNEVENTFULLY. MX WAS SENT TO INSPECT THE NR 1 ENGINE. PERFORMED INSPECTION FOR FLAMEOUT AS OUTLINED BY MM 72-00. PERFORMED NR 1 ENGINE OVERSPEED GOVERNOR CHECK IAW GE SEI-187. NO DEFECTS WERE NOTED AND THE ACFT WAS RELEASED FOR TEST FLIGHT AND PERFORMANCE OF MAX ALTITUDE ACCELERATION TEST. ON SUBSEQUENT TEST FLIGHT THE ENGINE FLAMEOUT OCCURRED AT FL310 WHILE SETTING UP THE MAX ALTITUDE ACCELERATION TEST. TEST FLIGHT CONDUCTED WHILE ENROUTE AND ENGINE WAS RELIT AT FL280. ACFT CONTINUED AND LANDED WITHOUT INCIDENT. SUBSEQUENT INSPECTION OF ENGINE USING A BORESCOPE, DETERMINED NUMEROUS (20+) FIRST STAGE TURBINE BLADES HAD FD. ENGINE WILL BE REPLACED AND SENT FOR SHOP VISIT.