While I'm not one to accept concepts without some type of testing, I can give some incite to the topic mentioned above.
It's been discussed before, and I've brought the idea up on another site as well, about a potential system check that forces HQ results when certain conditions are met, completely disregarding controlled factors.
I believe this is to be true on certain pieces, but not specific pieces in general. As some know, and I've stated in the past, I've been able to predict my haubergeon HQ's down to a 2-4 window for my last 6-7 haubergeon HQ's (That's about 60-70 haubergeon synths), these among other pieces as well like clockwork. My last 3 haub +1's I've hit down to a 1/1 window, no lie. This by no means, means I can continue to do this, but with the 2-4 window pattern I see and know, it is possible. This pattern has recently been proven to work (specific for myself), regardless of set or controlled factors.
When crafting larger batches (36-48 batches) of items, notice:
1.) How materials "Lost" are compensated among your stacks. Over time they seem to be "Lost", distributed evenly among your material stacks, or very close. You see this the larger your batch.
2.) How averages of HQ's are met over time, more-so with larger batches.
If your one to believe in a dataset table as mentioned in this thread, I've called out potential averages.
The idea about this post is "What if I hit NQ or Fail zone all the time?" I believe there to be some chance the system compensates for all these Fails and NQ's, and forces an HQ when needed, completely disregarding controlled factors.
Now I've gone 3 HQ's in a row on haubergeons and I've gone 2-3 fails in a row on haubs, but I have yet to have one HQ - not to appear on average 1 in 10 synths. This is only one of few pieces I use as example.
Has anyone synthed enough to notice that Fail zones appear on average 5-10%, 10% more-so among more valuable, higher tier pieces. With enough testing, these averages appear much more consistant with one another regardless of piece.
With SE's system of failure, a system that forces you to fail 5-10% on average, why shouldn't SE force a system that makes sure you HQ once a certain condition met, after you've synthed however many items? You and I know that we would not continue synthing, should we never have a shot at HQ correct? SE has a system which enforces this to happen over time. This is how we know we will eventually HQ.
Please don't misunderstand the concept behind this. I'm not saying that it's not possible to HQ "X" amount of times in a row or whatever. I'm saying, should you NQ or fail so many times in a row, the system compensates and forces an HQ due to your (bad luck, blah, blah, w/e). It makes sure the average is met! There it is.
With that, meaning the more Fails and NQ zones you see, the closer you are statistically to HQ.
There's a lot of pie in the sky speculation about what I mention, and there are people that have gone forever without HQ. Nothing mentioned above is absolute aside from myself predicting the window of HQ for myself.
While this has been discussed, it by no means has been proven on a public standpoint to exist.
Your best course of action is to notice, document, and test. You will see patterns, I promise you. No one including myself can tell you what works for yourself.
All my knowledge came from reading topics, testing, and my own personal experiences. These ideas, concepts, and patterns come when you elevate yourself to the point where you've synthed through a large enough sample to know what seems right, what seems wrong, and notice which patterns appear for discussion and testing.