I really don't think you'd produce anything of statistical significance trying to track such data.
I don't know about statistics, but there are certainly cases out there that merit closer investigation of an instructor or examiner, where clearly the instruction given and the check rides are sub par.
Some of those may be certificate mills, or some simply very poor instructors. I've met a few of them, and I'm sure you have too.
I know one designated examiner who makes no bones about recommending that low time pilots falsify their logbooks. I know this because he told me so. He's long been a certificate mill, though I don't know if he's still working or not.
I've known mechanics who turned out such shoddy work as to have killed people, and not just on a one-time basis, but who continued working and presenting a safety threat to the public for many years.
It's easy to make observations of an instructor who has students who aren't passing. It's not so easy to make a correlation between instructors and students, especially some years after the fact.
I had two students many years ago, both of whom were commercial pilots, whom I checked out in a Cessna 210. I made it very clear to both of them that the airplane had long range tanks, and that filling to the bottom of the filler neck would leave each tank one hour shy. Filling both tanks that way left the airplane two hours short of what they might expect to have.
Both pilots managed to run the airplane dry and make landings short of their destinations, on different occasions. I can't verify it, but was told that one of the two did it twice, which would make three occurrences of fuel mismanagement/starvation/exhaustion, with one common denominator: the instructor (same airplane, I believe, but you can't blame the airplane for unwise pilot actions).
Should the FAA look closely at me because I provided instruction to them? I checked them out in the airplane and gave them specific instruction, including strong counsel to not burn the tanks low, and to verify that they had adequate fuel, including multiple warnings about not having full tanks even if the tanks looked full from the top. We discussed strategies for ensuring the tanks were properly filled or for tracking their fuel load, including using a calibrated dipstick before filling, keeping fuel logs, timing the tanks, and other methods.
I kept good records of my instruction, as I always have. I could show exactly what I told them, what was covered. It was all written down. Never the less, those events could have easily been fatal...would that be an instructor error?
I checked a different person out at a different location. I received a phone call by the FBO that rented him the airplane, where I had checked him out, about a year and a half later. It seemed the individual had crashed an airplane at a remote airfield. He had neither a current medical nor a current flight review. The owners of the airplane were having trouble with the insurance company; they refused to cover the airplane. The owners called me, advising that because I was the last flight instructor to fly with the individual, I had a choice: back date the flight review to show that I gave him one, or be suborgated into the impending law suit.
I refused to falsify the record, and made it clear that I didn't give him a flight review. I gave him a courtesy check-out in the 172 for the flying club, and that was all. I had training records of my own, however, which showed that I clerkly advised him that he always needed to be current with respect to recency of experience, and that I'd reviewed those requirements with him, as well as a reminder that he always needed at least a third class medical certificate. In the end, it was my records that saved my fiscal bacon, and the other parties decided not to include me in their legal wranglings.
There are certainly cases where tracking an aviator's history and matching it with an instructor or examiner might prove useful, but finding the infrastructure to do this would be very problematic (I had seven instructors before I got my private...which one is liable?), as would the time-association (at what point is the pilot considered on his own, and no longer tied to his former instructor's apron strings?). In the last year I've flown with, received instruction from, or been examined by a dozen or so different instructors and check airmen. If I do something wrong, who gets blamed?
Me.
As it should be. There's a reason we are designated as "Pilot in Command," is there not?
