What is acceptance sampling?
Acceptance sampling decides whether to accept or reject a lot from the inspection of a random sample. It is used for incoming inspection, final inspection and supplier audits when 100% inspection is too costly or destructive. Sampling does not improve quality: a capable, stable process (see process capability) and supplier controls do. Sampling only checks that the process delivered what was expected.
AQL tables: ANSI/ASQ Z1.4 and ISO 2859-1
The tables first map the lot size and inspection level to a sample size code letter (general levels I, II and III; special levels S-1 to S-4 for small samples). The code letter and the AQL then give the sample size and the acceptance (Ac) and rejection (Re) numbers. The standards also define switching rules: move to tightened inspection after 2 of 5 consecutive lots are rejected, and back to normal after 5 consecutive lots are accepted. Reduced inspection is optional. This tool covers single sampling for normal inspection.
Sampling plan example
A lot of 2,500 molded caps is inspected at general level II with AQL 1.0%. The code letter is K: inspect 125 caps, accept the lot with 3 or fewer defectives, reject it with 4 or more. Lots at the AQL are accepted 96.7% of the time. Lots with 5.2% defective are still accepted 10% of the time (the LTPD), and with rectifying inspection the outgoing quality never averages worse than about 1.5% (AOQL).
Designing a plan from risks
When there is no standard to follow, specify the quality you want to accept (AQL with producer's risk α, typically 5%) and the quality you want to reject (LTPD with consumer's risk β, typically 10%). The design mode finds the smallest single sampling plan that meets both. For example, AQL 1% at α = 5% and LTPD 5% at β = 10% gives n = 132, c = 3.
How to use this Sampling Plans tool
- Choose the method. Look up an AQL plan, evaluate a plan you already use, or design a plan from risks.
- Enter the lot and AQL. For AQL plans, enter the lot size, the inspection level and the AQL.
- Read the plan. See the code letter, sample size and the accept and reject numbers.
- Check the protection. Read the OC curve: the acceptance probability at the AQL, the LTPD and the AOQL. Drag the probe for any quality level.
- Export. Export the plan and OC table to PDF or Excel for your inspection procedure.
Frequently asked questions
What is an AQL sampling plan?
An acceptance sampling plan tells you how many units to inspect from a lot (n) and how many defectives you may find and still accept it (Ac). AQL, the acceptable quality limit, is the worst process average that is considered acceptable; lots at the AQL are accepted most of the time.
How do I use ANSI/ASQ Z1.4 or ISO 2859-1?
Find the sample size code letter from the lot size and the inspection level (usually general level II). Then look up the sample size and the acceptance and rejection numbers for your AQL in the single sampling table for normal inspection. Arrows in the table point to the plan to use instead. This tool does the lookup for single sampling, normal inspection, for AQLs from 0.010% to 15%.
What is an OC curve?
The operating characteristic curve shows the probability of accepting a lot for every possible level of incoming quality. A steep curve discriminates well between good and bad lots. It shows the real protection a plan gives, which the AQL alone does not.
What are producer's and consumer's risk?
The producer's risk (α) is the chance of rejecting a good lot, at the AQL. The consumer's risk (β) is the chance of accepting a bad lot, at the LTPD (lot tolerance percent defective, also called RQL). The design mode finds the smallest plan that meets both risks.
What is AOQ and AOQL?
With rectifying inspection, rejected lots are 100% inspected and defectives replaced. The average outgoing quality (AOQ) is the average defect rate after inspection; its maximum over all incoming quality levels is the AOQL, the worst average quality that can leave the inspection.
Does accepting a lot at AQL 1.0 mean it has no more than 1% defective?
No. A plan accepts lots with a probability, not a guarantee. Lots with several times the AQL can still be accepted; check the LTPD on the OC curve. For critical characteristics, many companies use c = 0 plans or AQL 0.065 or lower.