What was found
DURING CLIMB APPROXIMATELY 10,000 FT BEGAN TO EXPERIENCE MULTIPLE AND RANDOM FMC ANOMALIES, VTK AND MAP WERE FIRST DISPLAYED ON CAPTAIN'S NAV DISPLAY, THEN ON F/O'S DISPLAY. BOTH CDU'S CYCLED REPEATEDLY BETWEEN THE MENU PAGE AND FMC PAGE. THIS SEEMED TO REPEAT SEVERAL TIMES AS IF BOTH FMC'S WERE RANDOMLY FAILING AND RESETTING. EVENTUALLY THE RIGHT FMC FAILED. QRH PROCEDURE FOR RIGHT FMC FAILURE WAS FOLLOWED AND NORMAL OPS WAS RESTORED. GROUNDED - YES. PERFORMED FMC TEST ON #2 PER B737-900 FIM 34-61 TASK 807. FAULT CLEARED. NO DEFECTS NOTED AT THIS TIME. A/C OK FOR SERVICE.