If all lots of materials coming into your inspection process were of perfect quality, the concept of AOQ would be moot since perfect incoming lots would mean perfect outgoing lots from inspection.

However, this may not always be the case.

We will examine what AOQ is, how the AOQ curve is developed, and the benefits and importance of your inspection and sampling procedure to prevent defective products from getting into your manufacturing process — or out to your customer.

## Overview: What is AOQ?

AOQ is defined as the expected average quality level of outgoing products coming out of inspection as a function of the quality of incoming products going into inspection.

AOQ is often represented in an AOQ curve. The AOQ curve shows the relationship between the quality of the incoming material and the quality of the outgoing material. It assumes rejected lots are 100% inspected, and defective items are either removed, reworked, or replaced. AOQL (average outgoing quality limit) is the maximum defective rate for the average outgoing quality.

A simple AOQ curve looks like this:

A more complex curve specifying sample sizes is shown below.

Note there are different curves depending on the sample size used in the inspection of incoming products. For a given level of incoming percent defective, the AOQ will decrease as the sample size increases. As sample size increases, AOQ is better than the incoming quality as a result of the 100% inspection of rejected lots and the removal of defective items. The AOQ curve initially increases as more defectives are produced. As more and more lots are rejected, 100% inspection becomes more common, and the AOQ curve starts to decrease at a rapid rate.

The formula for calculating AOQ is:

**AOQ = [(N x Pd x Pa) – (n x Pd x Pa)] / N**

Where:

**Pd**= percent defective in each lot**Pa**= probability of accepting a lot with a given Pd**N**= lot size**n**= sample size of each lot

ATI (average total inspection) is the average total number of items inspected and depends on the incoming quality, probability of acceptance, and the lot and sample sizes. When your incoming quality has no defectives, then inspect the specified sample size. When the incoming quality has many defectives, you must do a 100% inspection. Because quality levels vary between lots, the average number of items inspected over many lots will fall between 0% and 100% of the lot size.

The ATI curve shows the relationship between the quality of the incoming material and the number of items that need to be inspected, assuming that rejected lots will be 100% inspected and defective items will be removed, reworked, or replaced.

Below is an ATI curve.

## 3 benefits of AOQ

It would be great if your AOQ was 0%, but that’s rarely the case. Here are some benefits of knowing the value of your AOQ.

### 1. Defines the quality of your output

AOQ is the expected average percent defective of your outgoing product after inspection and replacement of a bad product. This is a good descriptor of the process performance of your supplier or your process.

### 2. Aids in the selection of the most appropriate inspection strategy

AOQ is linked to the concept of acceptance sampling and can be used to determine the optimal sample size for inspection.

### 3. The AOQ curve

The AOQ curve can be used to visually represent the relationship between expected average incoming and outgoing quality.

## Why is AOQ important to understand?

AOQ is a good indicator of quality, so it’s important to understand how to interpret it and work to improve it.

### Quality of your supplier

Using incoming inspection and calculating AOQ to determine the quality of your supplier provides quantitative data to discuss quality concerns with your supplier.

### Link to acceptance sampling

Using the AOQ and ATI curves will allow you to sample the correct number of incoming items so you have assurances you will be able to determine whether to reject a lot or not.

### Relationship between incoming and outgoing quality

When the incoming quality level is high (low percent defective coming in), the AOQ is also high (low percent defective going out). Good material coming in means good material going out.

AOQ will peak when the incoming quality level is low to marginal. AOQ improves as the incoming quality level deteriorates because the incoming lots are rejected, 100% sorted, and the defectives are replaced with good product.

## An industry example of AOQ

Juicy Juice company did an incoming inspection of its bottles. Bottles were received in lot sizes of 5,000. The quality control (QC) department had been using a sample size of 35 with an acceptance number of 2. That is, if there are more than two bad bottles, the lot is rejected, and a 100% inspection is done with the bad bottles being replaced before sending the lot to production.

Historically, the supplier has had an incoming defective rate of approximately 5%.

Recently, production has been complaining they seem to be receiving more defective bottles than before. Using the AOQ curve below, you can see that an incoming defective rate of 5% will translate to an AOQ of approximately 3.6%. The production manager informed QC it was not acceptable.

By switching to a sample size of 55, the AOQ dropped to approximately 2.4%.

While this helped reduce the rejections in production, it was additional work for QC. The plant manager set up a meeting with the bottle supplier to discuss how they were going to improve their process, or else Juicy Juice would seek a new supplier.

## 3 best practices when thinking about AOQ

Here are some suggested best practices when using AOQ to understand your quality level.

### 1. Measurement System Analysis (MSA)

You need to be sure your inspection processes are capable of providing repeatable and reproducible outcomes so your calculations are correct and decisions appropriate.

### 2. Use OC, AOQ, and ATI curves

Use these curves to have a visual picture of the appropriate sample sizes and quality levels.

### 3. Acceptance sampling

Develop an understanding of the different sampling schemes to determine the best form of acceptance sampling to use for your organization.

## Frequently Asked Questions (FAQ) about AOQ

### 1. What is AOQ?

AOQ stands for average outgoing quality, which is the expected average quality level of outgoing product for a given value of incoming product quality.

### 2. What is the difference between AOQ and AOQL?

AOQL is the average outgoing quality limit and represents the highest value or percent defective for AOQ for a given level of incoming quality. It is the peak of the curve when displayed on an AOQ curve.

### 3. What is the relationship between AOQ and ATI?

AOQ (average outgoing quality) is the expected outgoing average percent defective after inspecting incoming materials or product. ATI (average total inspection) represents the relationship between the quality of incoming material and the number of items inspected, assuming rejected lots will be 100% inspected and defective items removed, reworked, or replaced.

## Summing up AOQ

Average outgoing quality (AOQ) is the expected average quality level of an outgoing product for a given value of incoming product quality after an inspection is performed on the incoming product. An AOQ curve represents this relationship.

When incoming lots are of high quality, the outgoing quality will also be good. When the incoming lot contains defectives, the outgoing quality will still be good because lots are inspected 100% and defective products are fixed or replaced.

The graph below shows the relationship between incoming quality and outgoing quality.