AN ACR LGT TAXIED IMPROPERLY AT DTW.

Narrative

AFTER ARRIVING IN DTW METRO AND EXITING RWY 3L ON YANKEE 5; WE WERE INSTRUCTED TO CROSS THE OUTER; TURN R ON WOLF AND HOLD SHORT OF RWY 27R. THIS WAS DUE TO CONGESTION ON THE RAMP NEAR OUR GATE. OUR NEXT INSTRUCTION WAS TO TURN R AROUND THE ISLAND TO JOIN THE OUTER; TO THE GATE. WE STARTED OUR TAXI AND; AS WE MADE THE TURN AROUND THE ISLAND; BOTH THE COPLT AND I NOTICED THAT WE WERE APCHING THE HOLD SHORT LINE FOR RWY 3L; THE ACTIVE RWY. WE STOPPED SHORT OF THE HOLD SHORT LINE; AND WERE ASKED BY GND IF WE WERE ON THE RWY. WE WERE NOT AND WERE INSTRUCTED TO HOLD OUR POS. WE WERE THEN GIVEN INSTRUCTIONS TO PROCEED ONTO RWY 3L; R TURN ON VICTOR; JOIN THE OUTER TO OSCAR 11; TO THE GATE. WE CALLED THE TWR SUPVR. HE INFORMED ME THAT WE MISSED THE TURN ONTO THE OUTER. WE NEVER SAW THE TURN; BUT ON TAXI OUT FOR OUR NEXT FLT; WE FOUND THE SUPVR'S POS TO BE CORRECT. FOR REASONS UNKNOWN TO US; WE DID MISS THE TURN. I BELIEVE THE POSITIONING OF THE TXWY LIGHTS; AND OUR ANGLE TO THEM; CONTRIBUTED TO THE MISSED TURN. ADDITIONALLY; THIS ISLAND IS NOT DEPICTED ON THE COMMERCIALLY SUPPLIED ARPT PAGE 10-9 DTW.