AVRO RJ85 HAS ENG FAILURE DURING TKOF AND CONTINUE TO DEST.

Narrative

DURING TKOF GND ROLL; ENG #4 'ENG VIBRATION' MASTER CAUTION ILLUMINATED. VIBRATION REGISTERED 1.9. THE TKOF WAS ABORTED. ALL ENG READINGS READ NORMAL; AND THE FO AND I FELT NO PHYSICAL VIBRATION. ONCE CLR OF THE RWY I TOLD THE FLT ATTENDANTS THAT WE DID NOT HAVE AN EMER AND ALSO MADE AN ANNOUNCEMENT TO THE PAX EXPLAINING WHY THE TKOF WAS ABORTED. I CALLED OUR DISPATCH AND TOLD THEM WHAT HAD HAPPENED. I THEN SPOKE WITH OUR MAINT CTL. MAINT CTL ASKED SEVERAL QUESTIONS SUCH AS; 'DID WE FEEL ANY VIBRATION?' 'DID ENG INSTS READ NORMAL/ABNORMAL?' I ASKED MAINT CTL IF OUTSTATION MAINT SHOULD BE CALLED AND MAINT CTLR STATED THAT HE HAS TO LOOK FURTHER INTO IT BUT THAT NO; OUTSTATION MAINT PROBABLY WOULDN'T HAVE TO BE CALLED. WE TAXIED BACK TO THE GATE AND DEPLANED THE PAX. I CALLED MAINT CTL AGAIN AT THE GATE AND MAINT CTLR ASKED AGAIN IF WE HEARD ANYTHING; FELT ANY VIBRATION OR SAW ANY ABNORMAL INDICATIONS ON THE ENG INSTS. I TOLD MAINT CTLR 'NO' AND THAT THE ENG INSTS READ NORMAL. MAINT CTLR STATED IT IS MORE THAN LIKELY A FALSE ALARM AND THAT IT IS PROBABLY A SENSOR PROB. UNDER THE DIRECTION OF MAINT CTL THEY WANTED ME TO START UP THE #4 ENG AND SEE IF IT STARTED NORMAL. I STARTED THE ENG; WHICH STARTED NORMAL AND I FELT NO VIBRATION IN THE THRUST LEVER. UNDER THE DIRECTION OF MAINT CTLR; THE VIBRATION SENSOR GAUGE WAS DEFERRED. I ASKED MAINT CTLR IF WE SHOULD TAXI OUT TO THE RWY WITH NO PAX AND APPLY SOME PWR TO SEE IF THERE WERE ANY ABNORMAL INDICATIONS OR VIBRATION. MAINT CTLR STATED 'NO.' EXTRA FUEL WAS ADDED AND OUR RELEASE WAS AMENDED. THE FO DID A WALKAROUND ON THE EXTERIOR OF THE ACFT AND STATED EVERYTHING LOOKED FINE. THE PAX WERE BOARDED AND WE TAXIED FOR DEP. ON THE TKOF ROLL; THE 'ENG VIBRATION' MASTER CAUTION ILLUMINATED ON THE #4 ENG. WHEN THE GEAR WAS RETRACTED THE FO AND I COULD HEAR A HIGH PITCH WHINING NOISE. WE WERE HANDED OFF TO DEP CTL AND STATED THAT TWR SAW A PUFF OF SMOKE FROM OUR R ENG. AFTER THAT XMISSION; OUR #4 ENG FAILED. I RELAYED THE INFO TO DISPATCH VIA ACARS AND IT WAS AGREED UPON TO CONTINUE TO DETROIT. I TOLD ATC WE HAD AN ENG FAILURE AND THAT WE NOT DECLARING AN EMER. PER OUR COMPANY A SINGLE ENG FAILURE IS NOT AN EMER ON THE AVRO RJ85. WE PASSED AROUND AN AREA OF HVY PRECIP AND HAD THE DTW ARPT IN SIGHT APPROX 15 MI FROM THE ARPT AND LANDED IN VFR CONDITIONS. AFTER THIS EVENT HAPPENED; I SHOULD HAVE EXERCISED OPERATIONAL CTL AND NOT HAVE DEPARTED BTV UNTIL A MECH COULD HAVE INSPECTED THE ACFT. I FELT THAT I WAS TAKING THE PROPER STEPS IN RPTING THIS TO MAINT CTLR; HOWEVER; WHEN MAINT CTLR WANTED ME TO START THE ENG UP AND LET IT IDLE; I SHOULD HAVE HAD A MECH DO THIS.