A B737-700 FLT CREW CONTINUES THEIR TKOF AFTER RECEIVING AN ACFT CONFIGN WARNING HORN AFTER THROTTLE ADVANCEMENT AT MDW.

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THIS WAS THE FIRST LEG OF A 3 DAY TRIP. WE TAXIED OUT FROM GATE TO RWY 4 ON A VFR MORNING. AS WE WERE CLRED TO CROSS RWY 31C ENRTE TO RWY 4; THERE WERE 3 ACFT AHEAD OF US IN SEQUENCE. THE TWR CLRED THE OTHER 2 ACFT FOR TKOF FAIRLY RAPIDLY. WE WERE CLRED INTO POS TO HOLD MUCH SOONER THAN WE EXPECTED. WE WERE PROBABLY ABOUT 3000 FT FROM THE HOLD LINE WHEN HE CLRED US ONTO HOLD. THE CAPT CALLED FOR THE BEFORE TKOF CHKLIST AS WE APCHED THE RWY. I ASSUMED HE HAD COMPLETED THE THROTTLE BURST SOMETIME DURING THE TAXI OUT; BUT I REALLY DON'T KNOW IF HE DID OR NOT. IT WAS MY TKOF AND WAS BRIEFED PRIOR TO TAXI. WE COMPLETED THE CHKLIST PRIOR TO ENTERING THE RWY AND WERE TOLD BY TWR TO BE READY; THERE WAS AN ACFT ON FINAL (3 OR 4 MI; I THINK). I TOOK CTL OF THE ACFT AND WAS CLRED FOR TKOF. WHEN I PUSHED UP THE THRUST LEVERS; THE TKOF WARNING HORN SOUNDED. I PULLED THE LEVERS TO IDLE. WE BOTH LOOKED AT CONFIGN; AND SAW THE TRIM; FLAPS AND SPD BRAKES HAD THE APPROPRIATE NORMAL INDICATIONS. HE SAID PUSH IT UP AGAIN; AND AGAIN THE HORN WENT OFF. I BEGAN TO PULL BACK THE THROTTLES AGAIN; BUT HE SAID 'EVERYTHING IS OK; GO AHEAD AND GO.' I PUSHED THE THROTTLES UP AGAIN AND AGAIN THE HORN WENT OFF. I SAID SET TKOF THRUST AND RELINQUISHED THE THROTTLES TO THE CAPT. HE ELECTED TO CONTINUE THE TKOF WITH THE HORN SOUNDING UNTIL WE LIFTED OFF. THIS ENTIRE EVENT OCCURRED VERY QUICKLY WITH THE ACFT NEVER PERCEPTIBLY SLOWING FROM THE INITIAL TKOF ROLL. I DID NOT APPLY THE BRAKES AT ANY TIME. I HAD 2 THOUGHTS IN MY MIND DURING THE SEQUENCE. THE DECISION TO ABORT RESTS WITH THE CAPT AND I WAS PRETTY SURE THE BOOK SAID NOT TO TAKE OFF WITH A TKOF WARNING HORN. AS I LOOKED BACK; I REALIZED I COULD HAVE APPLIED THE BRAKES AND STOPPED THE ACFT ON THE RWY; BUT I WAS EXPECTING THE CAPT TO MAKE THE ABORT DECISION. ONCE HE COMMITTED TO TAKE OFF; I WENT ALONG WITH HIS DECISION. I WISH I HAD BEEN MORE ASSERTIVE AND JUST STOPPED THE AIRPLANE ON THE INITIAL HORN SOUNDING; BUT I EXPECTED HIM TO TAKE THE ACFT WHEN I PULLED THE THROTTLES BACK AND TAXI OFF THE RWY. MY STRONG RECOMMENDATION IS TO MAKE THE 'THROTTLE BURST' PART OF THE BEFORE TKOF CHKLIST. IN THIS CASE WITH AN EXTREMELY EARLY CLRNC ONTO HOLD; WE WERE RUSHED TO THE BEFORE TKOF CHK AND MISSED THE THROTTLE BURST BEFORE WE GOT ON THE RWY. ONCE ON THE RWY; THAT INSIDIOUS 'GO MENTALITY' GOT THE BEST OF US. I MUST ASSUME THAT THERE WAS SOME SENSOR MALFUNCTION ON THIS B-700; BECAUSE WE BOTH SAW FLAPS AT 5 DEGS; TRIM IN THE GREEN AND THE SPD BRAKE STOWED. THE ACFT BEHAVED NORMALLY FOR THE REST OF THE DAY. I ALSO KNOW THAT PLTS SOMETIMES SEE WHAT THEY EXPECT TO SEE AND THAT'S WHY THE HORN IS THERE. WE SHOULD HAVE FOLLOWED THE PROCS AND TROUBLESHOT THE PROB ON THE TXWY AFTER ABORTING THE TKOF. WE SHOULD ALSO HAVE WRITTEN UP A MALFUNCTIONING ACFT SO SOME OTHER CREW ISN'T FACED WITH THIS SAME PREVENTABLE EVENT. I WILL NEXT TIME. SUPPLEMENTAL INFO FROM ACN 634114: CONTINUED THE TKOF BY MY COMMAND. TKOF WAS NORMAL. DOUBLE-CHKED THE CONFIGN AND BOTH PLTS AGREED IT WAS NORMAL. AS A NOTE; THIS WAS MY THIRD FALSE TKOF WARNING HORN IN THE B-700 ACFT. OTHER TWO WERE HIGH SPD HVY WT WARNING SOUNDED BTWN 80 KTS AND V1. IF WE ARE TO OBEY THE TKOF WARNING HORN; WE DESPERATELY NEED A DEPENDABLE TKOF WARNING SYS. WE WERE CLRED VERY EARLY FOR TKOF (STILL 2 ACFT ON THE TXWY AHEAD OF US) AND BEGAN THE BEFORE TKOF CHKLIST BEFORE WE HAD A CHANCE TO DO THE THROTTLE BURST. IF THIS WAS PART OF THE BEFORE TKOF CHKLIST; WE WOULD HAVE FOUND THIS FALSE HORN BEFORE WE WERE CLRED FOR TKOF.