A representative from a sales department purchases pens from a vendor to give away at trade shows. Each shipment of pens has a lot size of 5000 pens. The sales representative wants to implement a sampling plan so that the entire lot of pens is either accepted or rejected. The sales representative and the vendor agree that the AQL for the sampling plan is 1.5% and that the RQL is 10%.

- Choose .
- From the drop-down list, select Create a Sampling Plan.
- In Measurement type, select Go / no go (defective).
- In Units for quality levels, select Percent defective.
- In Acceptable quality level (AQL), enter
`1.5`. - In Rejectable quality level (RQL or LTPD), enter
`10`. - In Producer’s risk (Alpha), enter
`0.05`. - In Consumer’s risk (Beta), enter
`0.10`. - In Lot size, enter
`5000`. - Click OK.

For each lot of 5000 pens, the sales representative should randomly select and inspect 52 pens. If more than 2 defectives pens are found, the sales representative rejects the entire lot. For 2 or less defective pens, the sales representative accepts the entire lot.

In this case, the probability of acceptance at the AQL (1.5%) is 0.957 and the probability of rejecting is 0.043. The sales representative and vendor agreed that lots of 1.5% defective would be accepted approximately 95% of the time to protect the producer. The probability of accepting at the RQL (10%) is 0.097 and the probability of rejecting is 0.903. The sales representative and vendor agreed that lots of 10% defective would be rejected most of the time to protect the consumer.

When entire lots are rejected, they are usually subjected to 100% inspection, with defective items replaced or reworked. This type of inspection is called rectifying inspection. Use the following metrics to understand the impact of 100% inspection and rework:

- The average outgoing quality (AOQ) represents the average quality of the lot after the additional inspection and rework. The AOQ level is 1.4% at the AQL and 1.0% at the RQL. The average outgoing quality limit (AOQL) = 2.603 at 4.300 percent defective and represents the worse case outgoing quality level.
- The average total inspection (ATI) represents the average number of inspected items after the additional inspection and rework. The ATI per lot represents the average number of pens inspected at a particular quality level and probability of acceptance. For the quality level of 1.5% defective, the average total number of pens inspected per lot is 266.2. For the quality level of 10% defective, the average total number of pens inspected per lot is 4521.9.