Date: 202103
Local time of day: 0001-0600
Location: HCF.TRACON, HI
Flight conditions: Marginal
Aircraft: Caravan Undifferentiated
Operator: Air Taxi
Flight plan: IFR
Mission: Passenger
Flight phase: Final Approach
Airspace: Class E HCF
ATC / advisory: TRACON HCF
Reporter organization: Government
Reporter function: Approach
Human factors: Confusion; Distraction
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Returned To Clearance
Contributing factors: Airspace Structure; Chart Or Publication; Human Factors; Procedure
Primary problem: Human Factors

Narrative: Aircraft X was holding at 4;000 feet at the missed approach fix (and also initial approach fix) for several instrument approaches at. They had already executed the Missed Approach Procedure once because of weather below minimums. The pilot advised me that they wanted to try again. Since they were already established in a holding pattern published for the ILS approach; I cleared them for the ILS approach and issued the altimeter.The procedure is clear that the only route of flight allowable from holding is via the 10 DME arc to a straight-in course on the localizer. That is what I expected them to fly. I quickly redirected my attention to a sequence of three other aircraft I was trying to shoot a gap with; through a band of weather. At the same time; I had another arrival that was opposite direction; outbound from the same gap. When I was able to finally scan back to Aircraft X I noticed that they were not on the 10 DME arc; and had strayed into a 4;000 foot Minimum IFR Altitude at 3;000 feet. My first thought was that they decided to shoot a different approach; but when queried; the pilot responded that they still planned the ILS. However; their current position did not correlate to any possible point on the Approach.When questioned further; the pilot said that they were direct to a fix to intercept the localizer. They had received neither a direct clearance nor a descent clearance. Without any more questioning; I informed them that the Minimum Vectoring Altitude (technically minimum IFR altitude) in that area is 4;000 feet; and issued a 'cancel approach clearance' and 'climb immediately; maintain 4;000 feet.' The MSAW (Minimum Safe Altitude Warning) did not activate. Because there was no audible alarm; and the fact that I knew 3.000 feet was still a safe altitude; I chose to not use the 'low altitude alert' portion of the phraseology. Later; after discussion with; and as recommended by the Operations Manager; I issued a warning to the pilot.Because this occurrence was a pilot deviation; there is not much from the ATC perspective that would have changed the outcome. Undoubtedly; the pilots' workload was high; due to the missed approach and bad weather. The design of the approach is also somewhat complicated because there are variations including the arc; published holding; and an outbound course on the localizer (which they apparently wanted to fly); but they don't all connect logically. However; the pilots should've queried if unsure.




Synopsis: HCF Approach Controller reported an aircraft deviated from the published approach procedure and flew below their Minimum Vectoring Altitude.