Oscar,
ChineseTiger1986 might be a bit reactionary but basically he's on the ball.
1. the Chinese engine issue, wherever the major problem may lie, is not QC, IMO.
China is World Factory for many reasons. While QC is always an issue for ANY country, it's very hard to comprehend, to the extent of being almost illogical to argue, that THE major issue with China's engine production is about QC.
The question is if QC is not an obvious problem of most Made-in-China high end consumer products(sure, it is the prob with many low end ones), why it is a problem for top line military production project like engine when China obviously takes the whole issue as the top priority?
One also can ask reversely that if QC is the major prob in China's top mil production line, then QC must also be the major problem in almost ALL Made-in-China high end consumer production lines. But it that true?
Furthermore, do you know how's the QC with China's Long March rocket engine production lines? They must be very bad as well following the same rationle of yours. Aren't they? And why not?
2. your Turkey example is not a rational comparsion here.
Engine design & production (including QC here) exemplifies the overall industrial sophitication of a nation, agree? Then is Turkey's industrial might across fields in your view a league ahead of China? More precisely, can you name one example of superior QC of indigenous Turkish high-end industrial production, military or civilian, vís-a-vís China?
What happens is that Turkey's F-16 engine production line is the exact line used in the US and imported from the original manufacturer. Turkey is told how to make every step precisely using the exact tools and procedures supplied by the US company and supervised step by step by on-field US engineers. Turkey's QC ratio, therefore, should be exactly the same as that of the US manufacturer in the US, theoritically speaking. Of course its QC is not a major issue, unless the Turks fall into sleep during the working hours.
While China has entirely different major issue from Turkey. It's likely to be true that China still can not mass-produce its engines at the moment. But in my understanding it's mainly due to lack of such experiences as how to get it right by trial & error in order to set the exact engine production line parametres and procedures right and precisely in the first place.
Saying that, I don't mean that QC is not an issue at all, but just not THE major one, for now, particualrly not in comparison to Turkey's F-16 engine that you brought on.
The right question here is, what do you think China's QC ratio vís-a-vís Turkey's would be if the exact F-16 engine production line, the related knowhow on production procedures and the same machine tools are shifted to China by the US company tomorrow?
Your China vs Turkey engine QC ratio in its nutshell is in fact China vs US on aero engine production and the general top-end industrial sophistication it associates with, nothing to do with Turkey per se.