Example of creating an attributes acceptance sampling plan

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 Stat > Quality Tools > Acceptance Sampling by Attributes.
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.

Interpret the results

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.

Measurement type: Go/no go

Lot quality in percent defective

Lot size: 5000

Use binomial distribution to calculate probability of acceptance

Method

Acceptable Quality Level (AQL)	1.5
Producer’s Risk (α)	0.05

Rejectable Quality Level (RQL or LTPD)	10
Consumer’s Risk (β)	0.1

Generated Plan(s)

Sample Size	52
Acceptance Number	2

Percent Defective	Probability Accepting	Probability Rejecting	AOQ	ATI
1.5	0.957	0.043	1.420	266.2
10.0	0.097	0.903	0.956	4521.9

Average Outgoing Quality Limit(s) (AOQL)

AOQL	At Percent Defective
2.603	4.300