Acceptance sampling

Acceptance sampling is a quality-control method that inspects a random sample from a batch and accepts or rejects the entire batch based on how many defects the sample contains.

What it is

See it move

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A batch of 500 units is sampled at n = 20, accepted only if none are defective. If the true defect rate is p = 5%, the probability all 20 sampled units are good is 0.95^20 ≈ 0.358, so the batch is accepted about 35.8% of the time and rejected the remaining 64.2%, even though the batch itself is only 5% defective.

The formula

LaTeX

P(\text{accept}) = (1-p)^n

Variables

$p$: True proportion defective in the batch (%)
$n$: Number of units inspected (sample size) (units)

For a plan that accepts the batch only if the sample contains zero defective units (c = 0); p is the batch's true proportion defective and n is the number of units inspected.