ICE ACCUMULATED ON THE INBOUND LEG IS REMOVED. AFTER THE SUBSEQUENT DEP AN ACR OBSERVER CLAIMS DE-ICE HOLDOVER PROCS WERE NOT COMPILED WITH.

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UPON ARR INTO SUX; FLT XXXX; I DETERMINED THAT IT WOULD BE NECESSARY TO DE-ICE THE ACFT; TO REMOVE THE ICE BUILDUP FROM THE INBOUND FLT. I ALSO DETERMINED THAT NO PRECIPITATION (RPTED LIGHT SNOW) WAS ADHERING OR ACCUMULATING TO THE AIRFRAME; THEREFORE; I DID NOT INITIATE A 'GND ICING PROGRAM.' HOLDOVER TIME CONSIDERATIONS WERE NOT APPLICABLE UNDER THESE SPECIFIC CONDITIONS; IN ACCORDANCE WITH AIRLINE'S WINTER OPS/GND ICING PROGRAM. AFTER WE HAD BEEN DEICED WITH TYPE 1; TO REMOVE THE ACCUMULATED ICE FROM THE INBOUND FLT; WE (THE FO AND I) DETERMINED THAT THE ACFT WAS FREE OF ANY SNOW; FROST OR ICE; VIA A VISUAL INSPECTION FROM THE COCKPIT AND TAXIED OUT. ALL THIS WAS ACCOMPLISHED UNDER NORMAL CONDITIONS (AT NO TIME DID WE ENTER GND ICING CONDITIONS). AFTER TAXIING TO THE END OF THE RWY AND PERFORMING A PRECAUTIONARY TKOF CHK; I DETERMINED THAT IT WAS SAFE TO TAKE OFF AND CONTINUE TO STL IN COMPLIANCE WITH FAR 91.527 AND FAR 121.629. HOLDOVER TIMES WERE UNNECESSARILY XMITTED FROM STATION OP WHILE INFLT; ALTHOUGH THEY WERE NEITHER REQUESTED NOR REQUIRED. AN FAA INSPECTOR ONBOARD; RIDING ON THE OBSERVATION SEAT; QUESTIONED THE DEICING PROC AND HOLDOVER TIME AFTER WE DEPARTED SUX. I BELIEVE THAT NO PROC; RULE OR REG HAS BEEN BROKEN OR OVERLOOKED AT SUX; DURING DEICING AND TKOF. SUPPLEMENTAL INFO FROM ACN 536890: UNDER OUR COMPANY WINTER OPS ICING PROGRAM THERE ARE 2 PROGRAMS UNDER WHICH WE OPERATE; NORMAL AND GND ICING. NORMAL REQUIRES ONLY TYPE 1 AND DOES NOT REQUIRE COMPLIANCE WITH HOLDOVER CHARTS. WE WERE OPERATING UNDER THIS NORMAL PROGRAM. THE FAA INSPECTOR ON BOARD SAID WE EXCEEDED OUR HOLDOVER TIME AND TOOK OFF IN VIOLATION.