AN MDT ACR CREW HAD PART OF THEIR R ENG COWLING FLY OFF DURING TKOF.

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THE ACFT WE WERE FLYING HAD JUST HAD MAINT PERFORMED ON THE R ENG'S FUEL SYS. TO DO THAT; THEY REMOVED THE UPPER R PART OF THE ENG COWLING. UPON FINISHING THE REPAIR AND CLRING THE WRITE-UP; THE FO AND MYSELF HEADED OUT TO THE ACFT. HE (FO) HAD TO RUN BACK IN FOR SOMETHING SO I WENT OUT PERFORMED A WALK AROUND AND VISUALLY CHKED THE COWL TO MAKE SURE IT WAS SECURE. ALL FASTENERS THAT I COULD SEE WERE LINED UP WITH THE MARKS ON THE COWL (TO SHOW THEY WERE SECURE); AND I ALSO PUSHED ON THE COWL WITH NO MOVEMENT NOTED. I GOT INTO THE ACFT AND THE FO CAME OUT AND HE ALSO CHKED THE ACFT; INCLUDING THE COWLING. WELL YOU CAN SEE WHAT COMES NEXT. ON TKOF AND INITIAL CLBOUT THE SAID COWLING PIECE CAME OFF INFLT. WE NOTED NO ABNORMAL VIBRATIONS OR ANYTHING -- RETURNED TO STL WITH NO FURTHER INCIDENT. HOW TO CORRECT THIS. I DON'T KNOW. SHORT OF ME GOING OUT WITH A SCREWDRIVER AND CHKING EVERY TURN/LOCK CONNECTOR ON THE ACFT. TO A LARGE EXTENT; WE RELY ON THE MECHS SIGN OFF AND FAITH THEY DO THEIR JOBS 100 PERCENT RIGHT. BUT IT IS A REAL WORLD OUT THERE. I DID MY PART -- LOOKING AT THE COWL; CHKING WHAT FASTENERS I COULD AND TOUCHING SAID COWLING WITH NO MOVEMENT NOTED.