1) Establish lower AQL restrictions (but the supplier might refuse)
I know of a large clothing firm that puts the AQL limit for serious faults at 0.65%. Most individuals (particularly suppliers) believe it is unprecedented. Of course, the majority of garment factories refuse to cooperate with those enormous corporations. However, if your volumes are high and you are willing to tolerate a somewhat higher price, you can specify a lower AQL.
2) Define major flaw, minor defect, and “no defect” more precisely
This is less likely to be refused outright by the provider than lowering the AQL. Expect some pushback once they realize the effects (many problems classified more seriously than they believe is appropriate).
3) You could adhere to Inspection Level III
By selecting a higher inspection level (level II is the default level, which is used for approximately 90% of all product inspections), or possibly even higher (if you have access to Minitab, you can adjust the limiting quality as suggested here), you will be conducting stricter QC inspections by checking more samples, lowering the chances of defects slipping through.
A higher inspection level is ideal if your supplier’s quality is consistently bad, or if you have high-grade goods where quality errors just cannot be allowed.
4) Conduct a random inspection followed by a 100% inspection
You could start with a random inspection to identify any issues that appear to be recurring. Then, in a subsequent stage, you might perform a 100% check (on the entire batch) that just concentrates on the 1 or 2 most common problems discovered during the random inspection. (It takes significantly longer if you complete a 100% check for all problems.)
5) Request that your supplier collaborate with a consulting firm
If you are a relatively significant customer, you could ask the manufacturer to collaborate with a consulting firm to push changes. This manner, they will be able to implement the necessary process controls as well as a proper quality system.