ACR CREW PROGRAMS FMS INCORRECTLY. ARTCC NOTICES RTE DEV.

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RTE DEV OCCURRED ON A FLT FROM CLE TO ORD. THE FILED RTE OF FLT WAS CLE.SKY.VWV.OX1.OX13.ORD. THE ACFT IS EQUIPPED WITH DUAL FMS. WHILE PROGRAMMING THE FMS; THE CORRECT ROUTING WAS PUT IN UP TO THE OXI VOR. AT THAT POINT; ORD WAS INPUT AS THE DEST. WHILE PROGRAMMING THE FMS FROM THIS POINT; HOWEVER; THE VWV TRANSITION WAS INADVERTENTLY ADDED WHILE INPUTTING ARR AND RWY APCH DATA. THE FMS GOES THROUGH A SERIES OF PROMPTS; AND ASKS WHEN A STAR IS INPUT FOR A TRANSITION -- IF THERE ARE ANY. WHEN THE PROMPT CAME UP FOR TRANSITION; AND VWV WAS PRESENTED; BOTH THE FO AND MYSELF INPUT THE RTE VIA THE TRANSITION -- INCORRECTLY. ONCE AIRBORNE; WE FLEW VIA THE VWV TRANSITION FOR THE OX13 ARR. ATC ASKED US OUR ROUTING AND I READ IT DIRECTLY FROM THE RELEASE. THEY ASKED HOW WE GOT SO FAR S IF OUR RTE WAS VWV DIRECT OXI. IT TOOK US ONLY A MIN TO REALIZE WHAT WE HAD DONE. ATC GAVE US 3 VECTORS FOR TFC AND THEN DIRECT OXI. BOTH THE FO AND MYSELF LOOK BACK ON THE INCIDENT AND CAN SEE WHERE THE PROB OCCURRED. UNFORTUNATELY; WE BOTH AGREE THAT IT COULD HAPPEN AGAIN EASILY; UNLESS THE UTMOST VIGILANCE IS USED WHEN PROGRAMMING THESE COMPUTERS. SUPPLEMENTAL INFO FROM ACN 478530: IN THE PAST; WE HAVE UTILIZED THE TRANSITION. SUGGESTIONS: FULL READING OF CLRNC FROM ATC; LARGER PRINT ON FLT PLANS.