INADVERTENT ERRONEOUS RADIAL SET FOR INTERCEPT ON STAR. FOR RADIAL OF 343 DEGS; FLC SET 143 DEGS FOR THE INBOUND VICE 163 DEGS. CONSEQUENTLY THEY TURNED INBOUND TOO SOON.

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MADE PREMATURE TURN ON ARR. LOOKED AT ARR AND MISREAD RADIAL AND HDG. THE RADIAL WAS 343 DEGS WHICH WE SET AS 143 DEG HDG; INSTEAD OF 163 DEG HDG. EVEN THOUGH WE DID DOUBLE CHK THE CHART; PERHAPS THREE WOULD BE THE CHARM. ALSO; XCHKING SHOULD HAVE BEEN INCLUDED. SUPPLEMENTAL INFO FROM ACN 330520: I WAS BUSY WITH MY DSCNT AND APCH FLOWS; GETTING THE ATIS; ETC. THE CAPT AT FIRST QUESTIONED (IN HIS MIND; NOT VERBALLY) MY SET UP OF THE NAV RADIO BUT AFTER CONSULTING THE ARR PLATE SET UP HIS RADIO ON THE WRONG INBOUND COURSE AS WELL. AFTER APPROX 5 MI ON THE WRONG COURSE; CLEVELAND QUESTIONED OUR HDG. WE INFORMED HIM THAT WE WERE ON THE 343 DEG RADIAL TO DTW INBOUND (WE WERE ACTUALLY ON THE 323 DEG RADIAL). HE QUICKLY REALIZED OUR MISTAKE AND WE WERE GIVEN A HDG OF 080 DEGS TO INTERCEPT THE CORRECT RADIAL INBOUND AND AN AMENDED ALT OF 15000 FT MSL. BOTH THE CAPT AND I ARE RELATIVELY NEW ON THE AIRPLANE (DC9). WE WERE BOTH TIRED AFTER A COUPLE OF ROUGH WX DAYS. WE BOTH MADE AN HONEST MISTAKE OF TUNING IN 143 DEGS IN THE HSI (BECAUSE THE PLATE READS 343 DEGS). I BELIEVE FATIGUE AND WORKLOAD WERE THE MAJOR CONTRIBUTING FACTORS IN THIS EVENT.