B757 ON QUIET BRIDGE VISUAL TO RWY 28R ADVISED TFC 1 MI IN SIGHT. SLOWING TO 180 KTS; FO ADVISED R ENG EGT IN RED AND OIL PRESSURE IN RED. THROTTLE TO IDLE AND FLT ATTENDANT RPTED R ENG FIRE. HAD FO DECLARE EMER AND SHUT DOWN ENG AND CALLED FOR ENG FIRE CHKLIST. FLT ATTENDANT A DVISED STILL BURNING. HAD FO FIRE BOTH EXTINGUISHING BOTTLES. FIRE OUT ON TOUCHDOWN. EMER CREW CHKED FOR FIRE AND NONE NOTED. TAXIED TO THE GATE.

Narrative

JUST AFTER DARK ARRIVING VIA BIG SUR; VECTORS TO INTERCEPT QUIET BRIDGE VISUAL TO RWY 28R. JUST PRIOR TO SAN MATEO BRIDGE TOLD TO INTERCEPT RWY 28R CTRLINE AND ADVISED OF TFC APPROX ONE AND ONE HALF MI AHEAD FOR RWY 28L. CALLED 'TFC IN SIGHT;' REQUESTED HIS SPD; 180 KTS; SO WE SLOWED FROM 210 KTS ASSIGNED AND CONFIGURED FOR NORMAL LNDG. INSIDE BRIDGE AND DSNDING; FO ADVISED OF R ENG EGT RED AND R OIL PRESSURE RED. MOVED R THROTTLE TO IDLE AND DISENGAGED AUTOTHROTTLE. FLT ATTENDANT CALLED; RPTED 'R ENG IS ON FIRE.' DIRECTED FO TO NOTIFY TWR; DECLARE EMER AND REQUEST EQUIP. RECONFIGURED FLAPS TO 20 DEGS FOR SINGLE ENG APCH. HAD FO MOVE R FUEL CTL SWITCH TO CUTOFF AND START APU. FO CALLED FOR ENG FIRE CHKLIST. FLT ATTENDANT RPTED 'STILL BURNING.' I DIRECTED FO TO PULL FIRE HANDLE AND AFTER ANOTHER 'STILL BURNING' RPT; DIRECTED USE OF EXTINGUISHING AGENT. FIRE WAS RPTED OUT JUST PRIOR TO TOUCHDOWN AND I REQUESTED MONITORING. AS WE EXITED RWY; FLT ATTENDANT RPTED FIRE STILL OUT -- NONE VISIBLE. STOPPED ON TXWY T AND OBSERVED FIRE EQUIP APCHING RWY 28L COMING TOWARD US. MADE PA TELLING PAX OF FIRE INFLT ON R ENG; BUT NOW EXTINGUISHED AND WE WOULD REMAIN ON BOARD UNTIL CONFIRMATION BY FIRE DEPT IN ABOUT 1 MIN. AFTER TALKING TO FIRE DEPT AND CONFIRMING FIRE OUT WE REQUESTED TAXI TO GATE AND HAD EQUIP FOLLOW TO MONITOR AND PROVIDE ASSISTANCE IF NECESSARY. MY CONCERN IS THAT IN A BUSY ENVIRONMENT; AT NIGHT; I CALLED FOR ENG FIRE CHKLIST WHEN PERHAPS ENG FAILURE CHKLIST WOULD HAVE BEEN PROPER GIVEN THE ABSENCE OF FIRE WARNINGS IN COCKPIT. WE MIGHT CONSIDER A DECISION TREE THAT GIVEN A VERBAL RPT OF ENG FIRE ABSENT CONFIRMATION IN COCKPIT; WOULD CALL FOR TESTING FIRE WARNING SYS AND IF FUNCTIONAL; WOULD DIRECT US TO ENG FAILURE CHKLIST AND REFERRED TO 'TAILPIPE FIRE' AND CONSIDERATIONS.