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Single acceptance sampling plan is constructed to decide about a given lot meets a given quality criteria expressed as the actual fraction of non-conforming units in the whole shipment of N units – the Acceptable Quality Level (AQL). The methodology follows the standard ISO 2859-2. Statistical sampling procedures avoid 100% testing of all items (which may be too costly, or even impossible, e.g. in case of destructive tests). Therefore, only a randomly selected sample is tested for conformity and based on the number of non-conforming units in the sample, we decide about accepting or rejecting the whole shipment. Apparently, this decision may always be correct, or incorrect. The probability (or risk) of incorrect decision is a part of the acceptance sampling parameters defined prior to the sampling procedure by an agreement between supplier and consumer.
Two kinds of risk can be defined:
  • risk (probability) α of incorrect rejecting the shipment in which the actual number of non-conforming units lower than the agreed quality level and should have been accepted (so called supplier risk).
  • risk (probability) β of incorrect accepting the shipment in which the actual number of non-conforming units is in fact higher than the agreed quality level and should have been rejected instead (so called consumer risk).
It is indeed desirable for both α and β to be small. For a 100% testing both α and β would be zero. The sampling agreement seeks a compromise between risks (α and β) and testing cost which is a (perhaps linear) function of the number of tested units n, preferably n<<N.

PDF Single sample acceptance design - Pdf manual

Figure 1 illustrates a typical OC curve with a visualized sampling plan for a given (N=1000, AQL, RQL, α, β). If, for example, the actual QL of the lot was 0.08 (8%), the probability of accepting will be 80% (the dotted line). Computed values n=50 a c=5. Because n must be integer, there exists no OC curve that meets exactly the requirements (AQL, RQL, α, β). Therefore the real resulting risk must be recalculated for the corrected (rounded) n to give slightly different actual values α' and β'. The solution for c and n is taken such that α' ≤ α and β' ≤ β to ensure that the risk requirement is securely met. The AQL and RQL points are visible on the OC curve on Figure 1.

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