Acceptance Sampling by Variables - Compare

User-Defined Plans - Probability of Acceptance Table

The probability of accepting lots at the AQL should be close to 1 - $image\alpha.gif$ . The probability of accepting lots at the RQL should be close to $image\beta.gif$ . The probability of rejecting is simply 1 minus the probability of accepting.

Example Output

Compare User Defined Plan(s)

Sample Critical Defectives Probability Probability

Size(n) Distance(k) Per Million Accepting Rejecting AOQ ATI

100 3.44914 100 0.854 0.146 83.0 612.3

100 3.44914 600 0.224 0.776 130.8 2815.1

150 3.44914 100 0.899 0.101 86.1 500.1

150 3.44914 600 0.172 0.828 98.8 3007.3

200 3.44914 100 0.928 0.072 87.6 444.7

200 3.44914 600 0.135 0.865 76.3 3142.0

Sample Critical Maximum At Defectives

Size Distance(k) StDev(MSD) AOQL Per Million

100 3.44914 0.0027533 145.6 369.7

150 3.44914 0.0027533 138.5 288.9

200 3.44914 0.0027533 136.7 256.4

Z.LSL = (mean - lower spec)/standard deviation

Z.USL = (upper spec - mean)/standard deviation

Accept lot if standard deviation ≤ MSD, Z.LSL ≥ k and Z.USL ≥ k; otherwise reject.

Interpretation

For the camera data, the probability of accepting a lot at the AQL (100 defectives per million) at sample sizes of 100, 150, and 200 is 0.854, 0.899, and 0.928, respectively, which are all lower than 1 - producer's risk of 0.95. The probability of accepting a lot at the RQL (600 defectives per million) at sample sizes of 100, 150, and 200 is 0.224, 0.172, and 0.135, respectively, which is much higher than the consumer's risk of 0.10.

In this case, at the AQL, the probability of rejecting at the various sample sizes is 0.146, 0.101, and 0.072; and at the RQL, the probability of rejecting is 0.776, 0.828, and 0.865, depending on the sample size.