in fact,every mold factory have approval check list!I hink
As you,the most important is:try to shorten the cycle time (cooling layout)and mold size,the mold quality(hardeness,no sharpe,no impaction between mold components)!
you can also give a expexted cycle time to the mold factory for a...
if the insert was fixed in mold,i think maybe you need make a fixture for assembly!keep the fixture in the robot!
you shoud make a guide struction for the assembly!
