Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Flight Crew Last 90 Days 100; Flight Crew Total 8066; Flight Crew Type 1200
Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
ATC clearance was issued on the ground in ZZZ as follows: ZZZZZ 4 Departure ZZZZZ V3 MUE VECKI 9 Arrival; Maintain 10;000 feet; Squawk XXXX. Soon after getting airborne we were issued a vector 'heading 300.' We flew this heading with a new instruction to intercept the V3 to MUE. We were given another vector of '290' to intercept the V3 to MUE. This new heading navigated the aircraft over 'OKALA' intersection which our GPS was normally programmed for the VECKI 9 Arrival with an OKALA transition into PHKO. We were at cruising altitude of 10;000 feet. MEA is 8;400 feet. We made the turn over OKALA and intercepted V16 on the 075 degree radial to MUE at 10;000 feet. I refer you to the VECKI 9 Arrival which does not include intercepting the V3 between TIGAH intersection and MUE.HCF Control said we turned too early and have breached his 'HIGH TERRAIN CLEARANCE AREA and NOW ARE BELOW MINIMUM ALTITUDE.' 'TURN HEADING 300 OR YOU CAN GO DIRECT MUE.' We opted to go directly to MUE remaining at 10;000 (MEA is 8;400 feet).Our error was to turn early at OKALA instead of the controller required clearance wanting us to intercept the V3 from a heading of 290. Our altitude of 10;000 feet was above the High Terrain Clearance Area and complied with the MEA of 8;400.To prevent a recurrence or corrective action: Intercepting the V3 between TIGAH and MUE was an unusual routing since we normally go via OKALA to join the VECKI 9 Arrival; so we were reprogramming this route and were distracted from a controller request to get a radio check from Hilo. This partly contributed to us forgetting the unusual route (for us). Considering we needed to get the weather and NOTAMs into PHKO and prepare for the arrival route and the very short sector route to PHKO; we should not have accommodated the radio check request.
Air taxi Captain reported ATC issued a low altitude alert on arrival to PHKO due to an early turn.