A single-sampling plan has the following performance: What is the average outgoing quality limit if the sample size is 200 and the lot size is 6,000?

Question

A single-sampling plan has the following performance:  What is the average outgoing quality limit if the sample size is 200 and the lot size is 6,000?

Quizplus · Accepted Answer

To find the average outgoing quality limit (AOQL), we need to use the formula:
AOQL = (AQL + LTPD) / 2
where AQL is the acceptable quality limit and LTPD is the lot tolerance percent defective.

From the given performance, the AQL is 0.02 and the LTPD is 0.11.

Now, we need to find the probability of accepting a lot as good when the lot is actually bad, which is given by the formula:
P(accepting bad lot) = LTPD / (1-AQL)

Substituting the given values, we get:
P(accepting bad lot) = 0.11 / (1-0.02) = 0.1196

Therefore, the AOQL is:
AOQL = (0.02 + 0.1196) / 2 = 0.0698

To convert this into a fraction of the lot size, we divide it by the sample size:
AOQL = 0.0698 / 200 = 0.000349

Finally, we multiply this by the lot size to get the actual limit:
AOQL limit = 0.000349 * 6000 = 2.094

Therefore, the AOQL limit is greater than 0.0200 but less than or equal to 0.0220, which is option B.

A Single-Sampling Plan Has the Following Performance: What Is