Acceptance Sampling/Examples/200

Examples of Acceptance Sampling

Let the sample size be $200$.

Let the rule be to accept a batch for which the number of defectives $d$ is such that $d \le 3$.

Let the producer's risk $\alpha$ be the probability of the consumer rejecting a batch with $0 \cdotp 5 \%$ or less defectives.

Let the consumer's risk $\beta$ be the probability of the consumer accepting a batch with $5 \%$ or more defectives.

Then:

\(\ds \alpha\)

\(=\)

\(\ds 0 \cdotp 019\)

\(\ds \beta\)

\(=\)

\(\ds 0 \cdotp 009\)

Proof

This theorem requires a proof. In particular: Nelson says: "By appropriate statistical arguments". You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): acceptance sampling