AOQ Average Outgoing Quality Calculator
Acceptance sampling lets bad lots through some of the time. Average outgoing quality tells you how bad the product leaving inspection is on average. This calculator gives the probability of acceptance and the AOQ for a single sampling plan with accept number zero or one.
Your numbers
From your sampling plan. Must be no larger than the lot size.
Your results
Uses the binomial approximation, which is accurate when the sample is small relative to the lot. It assumes rejected lots are fully screened and defects replaced with good units. Treat results as planning estimates.
AOQ (percent defective) vs incoming defect rate
Sweeps Incoming defect rate p from 0.1 to 10, holding your other inputs fixed.
Track acceptance rates and AOQ by supplier
Optional: see how ERP inspection results can feed supplier quality reporting.
Optional. The tool and every export work without this. No spam.
How to use the calculator
Enter the lot size, the sample size and accept number from your plan, then the incoming defect rate you expect or want to test. Pa shows how often a lot at that quality is accepted. AOQ shows the average percent defective after inspection, assuming rejected lots are screened one hundred percent and defects removed. Drag the slider across defect rates and watch the chart: AOQ rises, peaks and then falls, because high defect rates cause most lots to be rejected and screened.
The formulas
For a single sampling plan with the binomial approximation, the probability of acceptance for c equal to zero is (1 - p) to the power n. For c equal to one it is that plus n times p times (1 - p) to the power n minus 1. Average outgoing quality with rectifying inspection is approximately p times Pa times (N - n) divided by N. The maximum of the AOQ curve is called AOQL, the average outgoing quality limit, which is the worst average outgoing quality the plan allows.
- Pa: probability of accepting a lot at defect rate p
- AOQ: p x Pa x (N - n) / N
- AOQL: peak of the AOQ curve across all p
Reading the result
With the defaults, a lot with 2 percent defective is accepted roughly half the time or more, and the AOQ is a fraction of the incoming rate. Scan the chart to find the peak, which is the AOQL for that plan. If the AOQL is higher than your customer allows, increase the sample size, lower the accept number or move to a more stringent plan. Zero acceptance plans have steeper curves at small p than c of one plans with similar sample size.
Common mistakes
AOQ only holds when rejected lots are screened and defects removed or replaced. If rejected lots are returned without screening, outgoing quality is not improved by the plan. Do not confuse AOQ with the AQL: AQL is a quality level the plan treats as acceptable, while AOQ is an outgoing average. For large samples relative to the lot, use the hypergeometric distribution. Also remember that sampling cannot guarantee a lot is defect free.
Frequently Asked Questions
What is average outgoing quality?
It is the average fraction defective in product leaving an inspection stage over many lots, when rejected lots are 100 percent screened and defects are removed or replaced. It depends on the incoming quality and the sampling plan.
What is AOQL?
The average outgoing quality limit is the maximum value of the AOQ curve across all possible incoming defect rates. It tells you the worst long-run average outgoing quality the sampling plan can allow when rejected lots are screened.
Why does AOQ drop at high defect rates?
Because most lots are rejected at high defect rates, and rejected lots are screened one hundred percent. So little bad product gets through. The worst outgoing quality happens at a middle defect rate where many lots are still accepted.
Does this work with ANSI Z1.4 plans?
It works for any single sampling plan with accept number 0 or 1, including such plans from Z1.4 tables. For larger accept numbers the binomial sum needs more terms than this calculator includes.
If you want sampling plans, acceptance rates and AOQ tracked per supplier inside your ERP, Netray can help build that reporting on your existing inspection data.
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