WRONG ARPT APCH; YIP VICE DTW.

Narrative

WE DEPARTED ORD HEADED FOR DTW. DSCNT DOWN TO 3000 FT IN PROGRESS; NAVAIDS ON ILS RWY 21R DTW. I WAS FLYING VISUALLY WITH NAVAID BACKUP ON HDG GIVEN BY APCH CTL. ALL 3 CREW MEMBERS WERE OUTSIDE VISUALLY SEARCHING FOR THE FIELD AND TFC. APCH CTL CALLS OUT ARPT TO OUR 3 O'CLOCK POS AND WE ESTABLISH A VISUAL AND COMMENCE A TURN TO THE RWY LIGHTS IN VIEW. I VISUALLY PICK UP RWY LIGHTS TO THE R RWY AND BEGIN TO ROLL OUT TO ALIGN MYSELF WITH THAT RWY. I DID NOT VISUALLY CHK MY NAVAIDS AT THAT MOMENT TO ENSURE PROPER ALIGNMENT AS I WAS IN THE TURN. BEFORE THE TURN WAS COMPLETE; APCH CTL TELLS US TO TURN BACK TO A HDG OF 090 DEGS AT 3000 FT AS WE ARE LINED UP ON WILLOW RUN AND NOT DTW. MOMENTS LATER DTW COMES INTO VIEW AND WE MAKE A NORMAL APCH AND LNDG. THE CAUSE FACTORS IN THIS INCIDENT THAT I SEE ARE: LAST LEG OF A WK-LONG TRIP INTO A LOC WE HAVE BEEN FLYING INTO FOR A WK UNDER IMC/VFR CONDITIONS (I.E.; PERCEIVED FAMILIARITY). MY NOT XCHKING THE NAVAIDS AS THE ARPT AREA AND RWYS CAME INTO VIEW (I ACCEPTED MY OTHER CREW MEMBERS' RECOGNITION OF THE ARPT WITHOUT MAKING MY OWN JUDGEMENT). LACK OF NOTIFICATION BY APCH CTL AS TO THE POSSIBLE LOCATION OF WILLOW RUN ARPT. CREW FATIGUE. SUPPLEMENTAL INFO FROM ACN 296919: CONTRIBUTING FACTORS: 1) VOR IN NAVAIDS INSTEAD OF ILS. 2) CLOSE PROX OF THE 2 ARPTS. 3) BOTH RWYS ON SAME HDG. 4) WILLOW RUN BEACON AND RWY LIGHTS WERE MUCH BRIGHTER THAN DTW.