Acceptance sampling uses measurements from a sample to decide whether to accept or reject a larger production lot.

It does not prove that every item in an accepted lot is conforming. It manages inspection effort and decision risk when full inspection is impractical, destructive or too costly.

A simple attributes plan might inspect $n$ randomly selected items and accept the lot if the number of nonconforming items is no greater than acceptance number $c$.

If the true nonconforming fraction is $p$ and independent sampling is a reasonable approximation, the probability of accepting the lot is

$$P(\text{accept})=\sum_{k=0}^{c}\binom{n}{k}p^k(1-p)^{n-k}.$$

For $n=20$, $c=0$ and $p=0.05$,

$$P(\text{accept})=(0.95)^{20}\approx0.358.$$

So even a lot with 5% nonconforming items has about a 36% chance of acceptance under this small zero-defect sample plan.

Two risks therefore matter:

• producer's risk: rejecting a lot of acceptable quality;
• consumer's risk: accepting a lot of poor quality.

Acceptance sampling is not a substitute for improving the production process. It is a lot-disposition decision layer, while process capability and control charts address how the process itself behaves.