Probability of Acceptance

Since is the probability of finding or fewer defectives in the sample, you can calculate the acceptance probability using the function PROBHYPR for Type A sampling and the function PROBBNML for Type B sampling.

For example, the following statements calculate for the plan , when sampling from a single lot of size that contains nonconforming items, resulting in a value of 0.0762970752:

data;
   prob=probhypr(120,22,20,1);
   put prob;
run;

Similarly, the following statements calculate for the plan , when sampling from a series of lots for which the proportion of nonconforming items is , resulting in a value of 0.1018322793:

data;
   prob=probbnml(0.18,20,1);
   put prob;
run;

Other Measures of Performance

The measures ASN, AOQ, and ATI are meaningful only for Type B sampling and can be calculated using the PROBBNML function. For reference, the following equations are provided.

Average sample number: Following the notation of Schilling (1982), let denote the probability of finding or fewer nonconforming items in a sample of size . Note that is equivalent to PROBBNML. Then, depending on the mode of inspection, the average sample number can be expressed as shown in the following table:

Average outgoing quality can be expressed as

if the nonconforming items found are replaced with conforming items, and as

if the nonconforming items found are not replaced.

Average total inspection can be expressed as