Quality Engineering Handbook by Thomas Pyzdek contains the line:

"It can be mathematically shown that acceptance sampling should never be used for processes in statistical control."

Anyone able to point to a reference showing this, or show the math, or offer an intuitive explanation?

I have a couple thoughts, but no specific reference or calculations.


If the process is in control and extremely capable, then every lot should be good. Any sampling plan has a chance of rejecting a good lot. In this case, all you achieve by acceptance sampling is to occasionally reject good lots. The control charts and capability calculations have already told you the lot was good, but you rejected it anyway!

At the other extreme, suppose the system is in control but not at all capable, so that all of the lots are bad. All you accomplish by sampling is to occasionally accept one of these bad lots. The control charts and capability calculations have already told you the lot was bad, but you accepted it anyway!

For in between cases it isn't so intuitive, but I can still imagine that that the overall quality of the accepted lots won't be particularly better than the overall quality of all the lots.



Another way to look at is to consider the measurements that determine control vs the measurements used for sampling. Typically, I expect that more measurements would be made for the control & capability calculations than would be used for sampling. The supplier presumably has measured 100's of parts over many days/weeks/months. The supplier has presumably measured several parts within your lot to know that they are behaving as expected. Why ignore that detailed, robust knowledge and instead use the meager knowledge based on a small sample from your lot?


Tim F

I have a couple thoughts, but no specific reference or calculations.


For in between cases it isn't so intuitive, but I can still imagine that that the overall quality of the accepted lots won't be particularly better than the overall quality of all the lots.

Yes me too can't give you a reference, but i certainly agree with Tim.
In addition, even if the process is only slightly capable capable (~0.90), but is in Statistical Control, i already have a rough information of what my percent non-conforming will be.
No need to check thru acceptance sampling if percent non-conforming increased, since i already know that my process is stable. Doing Acc0petance Sampling could only lead to Type I/Type II errors.

Though not a complete mathematical proof, this can be shown through the OC-curve: