What is the difference between AOQ and AOQL?

AOQ is the average outgoing quality at a specific incoming defect rate. AOQL is the maximum AOQ across all possible incoming defect rates — the worst-case scenario.

Why does AOQ decrease at very high incoming defect rates?

At high incoming defect rates, P(accept) is very low, so almost all lots are rejected and 100% sorted. After sorting, the outgoing quality is nearly perfect. Hence, very bad incoming quality paradoxically leads to very good outgoing quality.

Is AOQL applicable without 100% inspection of rejected lots?

No. AOQL assumes rejected lots are 100% screened and all defectives removed. If rejected lots are returned to the supplier or scrapped without screening, the AOQL concept does not apply.

How does lot size affect AOQL?

The factor (N − n) / N adjusts for the sample fraction. For large lots where N >> n, this factor approaches 1 and AOQL depends mainly on n and Ac. For small lots, the sample fraction is significant.

Can AOQL be used in quality contracts?

Yes. Specifying an AOQL in a quality agreement guarantees the average outgoing quality regardless of incoming quality fluctuations, providing a strong quality assurance commitment.

What is the Dodge-Romig approach?

Dodge and Romig developed sampling plan tables that minimize average total inspection for a given AOQL or LTPD requirement. Their AOQL tables are widely used in industries where rectifying inspection is practiced.

AOQL Calculator (Average Outgoing Quality Limit)

Calculate AOQL — the maximum average defect rate reaching customers after rectifying inspection. Evaluate worst-case outgoing quality levels.

Sample Size (n)

Accept Number (Ac)

Lot Size (N)

AOQL

1.57%

Max average outgoing quality

Peak Incoming Rate

2.80%

Where AOQ is maximum

Planning notes, formulas, and examples

About the AOQL Calculator (Average Outgoing Quality Limit)

Average Outgoing Quality (AOQ) is the average defect rate of lots that pass through a rectifying inspection scheme — one where rejected lots are 100% sorted and all defectives are replaced with good units. The AOQ depends on the incoming defect rate and the sampling plan's probability of acceptance.

The Average Outgoing Quality Limit (AOQL) is the maximum AOQ across all possible incoming defect rates. It represents the worst-case average quality that the customer will receive under the rectifying inspection approach. Regardless of how bad incoming quality gets, the outgoing quality after rectification will never exceed the AOQL on average.

This calculator computes the AOQ curve and identifies the AOQL for your sampling plan, providing assurance about the maximum average defect rate your customers will experience.

Integrating this calculation into regular operational reviews ensures that key decisions are grounded in current data rather than outdated assumptions or rough approximations from the past.

When This Page Helps

AOQL guarantees a maximum average outgoing defect rate regardless of supplier quality. It provides a quality assurance ceiling that protects customers and is especially valuable when incoming quality is unpredictable.

How to Use the Inputs

Enter the sample size (n) of your sampling plan.
Enter the accept number (Ac).
Enter the lot size (N).
Review the AOQL — the worst-case average outgoing quality.
Review the AOQ at various incoming defect rates.
If AOQL is too high, increase sample size or reduce accept number.

Formula used

AOQ(p) = P(accept) × p × (N − n) / N

AOQL = max AOQ(p) for all p from 0 to 1

where:
• P(accept) is from the binomial OC curve
• N = lot size, n = sample size

Example Calculation

Result: AOQL ≈ 1.8%

For n = 80, Ac = 2, N = 1,000: the AOQ peaks at approximately 1.8% occurring when the incoming defect rate is about 3–4%. Even if incoming quality is 10% or 20% defective, the average outgoing quality after rectification will be below 1.8%.

Tips & Best Practices

AOQL only applies when rejected lots are 100% screened and defective units are removed or replaced.
A lower AOQL requires larger sample sizes or tighter accept numbers.
Compare AOQL with your customer's quality requirements to ensure your plan is adequate.
The AOQL occurs at a specific incoming defect rate — both better and worse incoming quality produce lower AOQ.
Dodge-Romig AOQL plans are specifically designed to minimize inspection while guaranteeing a maximum AOQL.
Use AOQL as a selling point to customers — it puts a ceiling on the defect rate they will experience.

How AOQL Works

At low incoming defect rates, most lots pass inspection and AOQ approximates the incoming rate. As incoming quality worsens, more lots are rejected and sorted, limiting outgoing defects. The AOQ peaks at an intermediate defect rate — that peak is the AOQL.

AOQL in Practice

Rectifying inspection with AOQL-based plans is common in high-volume consumer goods where 100% sorting of rejected lots is feasible. The approach ensures consistent outgoing quality regardless of supplier variability.

Limitations of AOQL

AOQL is an average metric — individual lots that pass inspection may have higher defect rates than the AOQL. For single-lot protection, use LTPD-based plans instead. Also, AOQL assumes perfect 100% inspection of rejected lots, which may not be realistic for all defect types.

Sources & Methodology

Last updated: February 9, 2026

Frequently Asked Questions

AOQ is the average outgoing quality at a specific incoming defect rate. AOQL is the maximum AOQ across all possible incoming defect rates — the worst-case scenario.