CRJ-200 CAPTAIN AND DISPATCHER REPORT ANTI-ICE DUCT FAULT AND ICE DETECTOR FAILURES REQUIRING CREW TO AVOID ICING CONDITIONS; WHICH PROVES DIFFICULT. CREW FOLLOWS PROCEDURES FOR LANDING WITH ICE ON WINGS AND LANDS SAFELY.

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DURING CLBOUT IN ICING CONDITIONS AT ROUGHLY 11000 FT; WE RECEIVED AN ANTI-ICE DUCT MASTER WARNING AND AN ASSOCIATED ANTI-ICE DUCT AURAL WARNING. WE FOLLOWED THE QRH PROC WHICH HAD US TURN OFF THE WING ANTI-ICE AND THE 14TH STAGE BLEEDS AND LEAVE ICING CONDITIONS. WE THEN RECEIVED AN ICE DETECTION 2 FAIL STATUS MESSAGE. WE CONTACTED DISPATCH AND MAINT TO DETERMINE THE BEST COURSE OF ACTION CONSIDERING WHERE THE LEAST AMOUNT OF ICING WOULD BE. IT WAS DECIDED THAT WE WOULD CONTINUE ON TO ZZZ; AS ALL OF THE ARPTS IN OUR VICINITY WERE RPTED OVCST SKIES WITH ICING CONDITIONS. ZZZ WAS RPTING 1900 FT OVCST. OUR APU WAS ALSO INOP SO WE HAD TO PLAN ON AN UNPRESSURIZED LNDG. THE QRH PROC IS BASED ON WHETHER OR NOT THERE IS ICE ADHERING TO THE WINGS. IT LETS YOU RESET THE 14TH STAGE BLEEDS AND STANDBY WING SYSTEM A MAX OF 5 TIMES. WE DECIDED TO BE CONSERVATIVE AND ASSUME WE WOULD HAVE ICE IN THE DSCNT AND THAT THE SYS MAY BE ON AND OFF; SO WE PLANNED TO FOLLOW THE PROC WITH ICE ON THE WINGS AND LAND WITH FLAPS 20 DEGS RATHER THAN WAIT UNTIL THE LAST MIN WHILE ON THE ILS. THE QRH MAKES NOTE OF THE CRITICAL NATURE OF EVEN THE SLIGHTEST BIT OF ICE ON THE LEADING EDGE AND HOW THAT CAN AFFECT THE STALL MARGINS. EARLIER IN THE DAY WE HAD A WING OVERHEAT MASTER WARNING AND WING OVERHEAT AURAL ALERT IN THE SAME ACFT. THE ICE DETECTION 2 FAILURE HAD ALSO BEEN FIXED IN ZZZ1 EARLIER IN THE DAY SO WE COULD GET OUT OF ZZZ1. TAKING ALL OF THIS IN MIND; I THOUGHT IT BETTER TO BE ON THE SAFE SIDE AND ASSUME WE WOULD NOT HAVE WORKING DEICE SYSTEMS AND TO PLAN FOR ICE ON THE WING. FROM MY SEAT IT ALSO APPEARED THAT WE HAD ICE ON THE LEADING EDGE ALTHOUGH IT WAS NIGHT AND VERY DIFFICULT TO TELL. EVEN THOUGH WE HAD 9000 FT OF RWY; WE DECLARED AN EMER JUST AS A PRECAUTION. WE LANDED WITHOUT INCIDENT.