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A double sampling plan accepts or rejects on the first sample when the evidence is clear and draws a second sample only when it is ambiguous. Because most lots are decided on the smaller first sample, the average sample number is lower than a single plan of equivalent discriminating power.
Double sampling
Pa = P(accept on first) + P(go to second) x P(accept on second)
Average sample number
ASN = n1 + P(second sample) x n2
When inspection is expensive or destructive and most lots are clearly good or clearly bad. The saving in average sample size can be 25-40% against a single plan.
It applies to the combined sample. The cumulative count from both samples is compared with the second acceptance number, so it must scale with the larger total.