A TXWY AND RWY INCURSION WHEN AN MD80 CHK PLT AND HIS IOE FO FAIL TO NEGOTIATE THE R TURN ON TXWY P AND ALMOST ENTER THE CONFINES OF RWY 15 AT BWI; MD.

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WE WERE CLRED TO TAXI TO RWY 15R VIA TXWY P. TXWY P MAKES A 50 DEG TURN TO THE R AS YOU TRAVEL WBOUND. WE MISSED THE TURN AND CROSSED THE HOLD SHORT LINE FOR RWY 15R NEXT TO THE RWY 15R/RWY 10 INTXN. THE GND CTLR RECOGNIZED IT FIRST AND TOLD US TO STOP. THERE WAS NO ACFT ON RWY 15R; AND THANKFULLY THERE WAS NO CONFLICT. SOME CONTRIBUTING FACTORS WERE: 1) FO ON IOE ON THE PLANE. 2) WE WERE STOPPED ONCE BY GND CTL AS OUR GND CREW HAD LEFT A PANEL OPEN. 3) CREW WAS ACCOMPLISHING THE TAXI CHKLIST AT THAT TIME. WE BOTH HAD OUR GND TAXI CHARTS OUT AND OPEN; AND THE FO EVEN COMMENTED EARLIER HOW EASY IT WOULD BE TO MAKE A TAXI MISTAKE AT THIS ARPT. THERE IS ABSOLUTELY NO EXCUSE FOR THIS! A PLT NEEDS TO KNOW EXACTLY WHERE HE IS AT ALL TIMES ON THE GND OR STOP AND FIND OUT! I SAW THE FLASHING HOLD SHORT LINES COMING UP AND I EVEN MADE THE COMMENT THAT I WOULD NORMALLY HAVE THE FO VERIFY THAT WE ARE CLRED TO CROSS A RWY; BUT I 'KNEW' WE WERE OK BECAUSE WE WERE WATCHING A B737 LAND TOWARDS US ON THE PARALLEL RWY I THOUGHT WAS RWY 15R AND TURNED OUT TO BE RWY 10. BETTER RWY IDENT SIGNS MIGHT HELP. HOWEVER; I AM REDEDICATING MYSELF TO NOT JUST HAVE THE ARPT DIAGRAM OUT; BUT TO FOLLOW IT CLOSELY! I AM GOING BACK TO DOUBLE-CHKING WITH GND CTL BEFORE XING ANY RWY. SOMETIMES THEY SOUND A LITTLE ANNOYED WHEN WE ASK AGAIN; BUT THIS COULD HAVE BEEN A TRAGIC ACCIDENT!