why?
The volume can make a difference, I believe; but then other factors may come in play I guess. We here have abundance of suppliers and only a few and relatively little electronics manufacturers, so the suppliers make their best not to loose even a small good client.

I won't say you should move your production to Europe right away, though...

what?
So, if you definitively feel you do need an income inspection of parts, you shall consider some sort of testing for all parts, not only the '51. A defective resistor or capacitor or voltage regulator might IMHO cause smoke much more easier than a defective '51.

when?
If you want to do income inspection, I am afraid, you cannot avoid, so it's. On the other hand, this might open way to more effective testing methods than just running a test program, e.g. measuring I_CCQ and/or I_CCD, measuring I/O pin leakages, using various voltage/temperature conditions etc.

how?
As Erik pointed out, this sort of stuff is definitively not cheap and gets more expensive as more different tests you want to perform. You need to work out your economics, though.

I am afraid that it is questionable, whether a simple - and relatively cheap - software test, run on the assembled board straight from the '51, will cover enough possible modes of failure to be worth doing at all - especially if you didn't have identified any "typical" mode of failure (as I mentioned I wrote such a test but I knew how the failing part (mis)behaved).

JW