ENG LEFT RUNNING INADVERTENTLY.

Narrative

AFTER CLRING THE RWY AT DTW; WE TAXIED FOR GATE. THE CAPT HAD TO RECYCLE THE L REVERSER SEVERAL TIMES TO CLR AN 'UPLOCK' LIGHT ON THE REVERSER. HE THEN PROCEEDED TO SHUT DOWN THE R ENG AND I STARTED THE APU FOR PWR NEEDED AT THE GATE. IT PICKED UP R BUSS NORMALLY (AT LEAST I THOUGHT IT HAD). WE HAD RAIN; THE REVERSER PROB; TIGHT PARKING SPOT; BRIGHT RAMP LIGHTS AS DISTRS TAXIING IN TO GATE. THIS MAY HAVE CAUSED AN OVERLOOK OF THE R ENG STILL RUNNING. WE PARKED AT GATE AND THE CAPT SHUT DOWN THE L ENG AND CALLED FOR THE PARKING CHK. WHILE I WAS READING THE CHK; THE CAPT HAD TO GET CONFIRMATION OF 'CHOCKS IN;' AND WE HEARD A BANGING ON THE NOSE. RAMP GUYS HAD PLUGGED IN THE EXTERNAL PWR UNIT. THE CAPT SELECTED EXIT PWR AND BEGAN THE APU COOLING CYCLE; AND WE THEN COMPLETED THE PARKING CHKLIST. THE CAPT GOT UP TO GREET THE DEPLANING PAX AND GET THE NEXT FLT'S PAPERWORK. I COMPLETED THE LOGBOOK (FUEL AND TIMES); CHKED THE PWR AND TEMPERATURE ON THE APU AND SHUT IT DOWN. EVERYTHING APPEARED NORMAL WHEN THESE THINGS WERE DONE; AND I GOT UP TO LEAVE AND GO UP TO THE GATE TO CHK THE COMPUTER. AT THE GATE (A VERY SHORT TIME LATER) THE AGENT SAID MAINT WANTED TO TALK TO THE PLTS OF THE INBOUND FLT SO I WENT DOWN TO THE ACFT. A MAINT SUPVR WAS TALKING TO THE CAPT IN THE COCKPIT ABOUT AN ENG LEFT RUNNING. I COULD NOT BELIEVE IT; ESPECIALLY AFTER HAVING CHKED AND CHANGED PWR SOURCES. THE MAINT SUPVR SAID A MECH HAD COME UP TO THE COCKPIT AND SHUT DOWN THE R ENG AFTER WE (PLTS) HAD LEFT THE COCKPIT. APPARENTLY; WITH THE DISTRS AND THE TIGHT PARKING (OUR L WING UNDER A DC10'S WING); WE HAD BOTH MISSED THE FACT THAT THE R ENG WAS STILL RUNNING. I DO NOT HAVE THE HABIT OF CHKING THE SWITCHES AS I READ THE CHKLIST (AS PER SOPA) SO I CANNOT CONFIRM THEY WERE INDEED OFF. I CANNOT EXPLAIN HOWEVER; HOW I DID NOT SEE AN ABNORMAL ELECTRICAL CONFIGN ON 2 SEPARATE OCCASIONS AS THE ENG AC BUSS WOULD HAVE NOT BEEN PICKED UP BY EITHER THE APU OR THE EXTERNAL PWR UNIT; AND I SHOULD HAVE NOTICED THOSE BUSS LIGHTS OUT DURING PROPER OPS THAT NIGHT. I AM POSITIVE WE COMPLETED ALL THE CHKS THAT NIGHT AS REQUIRED BUT APPARENTLY MISSED THE R FUEL CTL SWITCH OFF. THE MAINT SUPVR DID TELL US THAT NO ONE WAS HURT NOR WAS ANY EQUIP DAMAGED BY THIS INCIDENT.