Different kinds of Hats inspection:

stripe hat
jacquard knitting hat
Jacquard knitting cap
knitting hat
kids baseball cap
sports cap
bucket hat
satin santa claus hat
winter hat with fleece lining
spandex beanie hat
pirate hat
Hair pin PVC sun visor
stretchable cap
Funky winter hat
polar fleece hat
Ribbon Floppy Hat
paper straw hat
Fedora hat
fleece hat
knitted pom pom beanie
Swimming Cap
fashion hat
beret
top hat
flat cap

Some common factors to check for Hats quality control:

Material:

Cotton
Polyester
T \ C
CVC
Nylon
Leather
velvet
Grass
PVC
Non-woven
paper

Hats composition:

Cap eyebrow 
Hat bodies
Oxygen hole
Top Button 
strap regulation
Anti-sweat Article 
Size strip
Reinforcement cap eyebrow
 

Size:

circumference
perimeter