MLG ACFT ON APCH IN MARGINAL WX CONDITIONS ENCOUNTERED WINDSHEAR AND FLC EXECUTED A MISSED APCH. DURING THE MISSED APCH THE FLC WAS FOLLOWING THEIR WINDSHEAR AVOIDANCE GUIDANCE SYS AND OVERSHOT THE MISSED APCH ALT BY 1000 FT. ATC CLRED THEM TO LEVEL AT 4000 FT.

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ON 15 MI FINAL; WE HEARD NUMEROUS ACFT AND TWR RPTS OF +/-20 KT AIRSPACE FLUCTUATIONS BY OTHER ACFT ON APCH. THE ACFT AHEAD OF US INITIALLY BEGAN A MISSED APCH AND THEN SAW THE ARPT AND CONTINUED ON IN TO LAND. WE WERE ON A 3 MI FINAL AND CLRED TO LAND WHEN WE RECEIVED AN 'INCREASING PERFORMANCE' WINDSHEAR ALERT BY OUR ONBOARD WINDSHEAR AVOIDANCE GUIDANCE SYS UNIT. WE EXECUTED A GAR; AND IN SO DOING; WHILE FOLLOWING OUR ONBOARD WINDSHEAR AVOIDANCE GUIDANCE SYS GUIDANCE; WE OVERFLEW THE MISSED APCH ALT (2800 FT MSL) AND EVENTUALLY LEVELED OFF AT 3800 FT MSL BEFORE THE ONBOARD WINDSHEAR AVOIDANCE GUIDANCE SYS GUIDANCE DISAPPEARED AND WE WERE ASSURED OF HAVING EXITED THE WINDSHEAR EVENT. WE CALLED THE MISSED APCH AND WAS TOLD TO LEVEL AT 4000 FT MSL AND TURN L HDG 180 DEGS FOR A VECTOR BACK FOR ANOTHER APCH. WE EVENTUALLY LANDED IN VMC CONDITIONS ON THE NEXT PASS; THOUGH WE HAD TO IGNORE MULTIPLE INCREASED AND DECREASED PERFORMANCE WINDSHEAR ALERTS TO DO SO; SINCE THERE WAS NO OTHER ARPT WHICH WAS LESS WINDY WITHIN RANGE OF OUR LIMITED FUEL SUPPLY. WE RPTED +/-20 KT AIRSPD FLUCTUATIONS ON FINAL TO THE TWR.