Small Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 7
Confusion; Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory
Airspace Structure; Human Factors; Procedure
Aircraft X departed OAK on the COAST RNAV Departure. I radar identified it and assigned an unrestricted climb to 10000 feet.  Then Aircraft Y departed SFO on the SSTIK departure. I radar identified it and climbed them to 4000 feet planning to crossover Aircraft X. At that time I noticed Aircraft X had turned south on his own out of 3000 feet putting him head on with Aircraft Y climbing through 2000 feet and rapidly merging. I immediately issued a right turn to Aircraft X heading 290 maintain 10000 feet. I advised Aircraft Y about Aircraft X and was able to get Visual Separation and assigned 3000 feet and a hard left turn to heading 230. As Aircraft Y started his left turn and dropped back to 3000 feet Aircraft Z departed Runway 28 at SFO climbing to 3000 feet. I radar Identified them and assigned maintain 3000 feet. I turned Aircraft Y right heading 260 and climbed them to 10000 feet and issued traffic about Aircraft Z. I issued traffic to Aircraft Z. I turned Aircraft Z left and gave a harder right turn to Aircraft Y but separation was lost. After all was settled and separation regained I issued a Brasher to Aircraft X.The Oakland departures have a turn depicted for the Loss of Communications. There have been numerous times when pilots misread the departure and turned. Usually it has been uneventful and we correct the situation and educate the pilot. This time was different. That south bound turn needs to be changed or removed from the departure; or depicted differently. I believe that is why Aircraft X turned south into a head on potentially mid-air situation.
The Controller states this is a somewhat regular mistake usually made by General Aviation aircraft.
NCT Departure Controller observed an aircraft fly the lost communication procedure for an RNAV departure which put it into confliction with other aircraft.