Light Transport; Low Wing; 2 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 20; Flight Crew Total 18000; Flight Crew Type 3000
Situational Awareness; Confusion; Workload
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Aircraft; Environment - Non Weather Related; Procedure; Weather
Cleared for the VOR/DME A approach 5500 Ft upon crossing BKA turned right to intercept 009 course inbound descending to 1800 then to 1000. After WINKA FAF continued to missed approach point at which point we had visual with the island but could not see the airport. Executed missed approach with climbing left turn at which time we got a terrain avoidance alert. MSA for the approach in the northern sector was 6600 ft. MSL. Elected to continue climb to satisfy terrain avoidance alert which remained illuminated through 6500 Ft. Over climbed the published missed approach altitude because of the terrain alert and conflicted with opposing traffic. We feel that we possibly had an erroneous terrain alert but due to being unfamiliar with the area and the terrain we felt the best action would be to continue our climb.
An air taxi flew the SIT VOR DME-A Approach and after executing a missed approach overshot the missed approach altitude because of terrain warning; possibly false; and conflicting traffic.