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You can use the base SAS functions PROBBNML and PROBHYPR to evaluate single-sampling plans. Measures of the performance of single-sampling plans include
For example, the following statements calculate P_{a} for the plan n=20, c=1 when sampling from a single lot of size N=120 that contains D=22 nonconforming items, resulting in a value of 0.0762970752:
data; prob=probhypr(120,22,20,1); put prob; run;
Similarly, the following statements calculate P_{a} for the plan n=20, c=1 when sampling from a series of lots for which the proportion of nonconforming items is p=0.18, resulting in a value of 0.1018322793:
data; prob=probbnml(0.18,20,1); put prob; run;
Average sample number: Following the notation of Schilling (1982), let F(c|n) denote the probability of finding c or fewer nonconforming items in a sample of size n. Note that F(c|n) is equivalent to PROBBNML(p,n,c). Then, depending on the mode of inspection, the average sample number can be expressed as shown in the following table:
Mode of Inspection | ASN |
Full | n |
Semicurtailed | |
Fully curtailed |
Average outgoing quality can be expressed as
Average total inspection can be expressed as
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