# Operating Characteristic (OC) Curve: Definition & Uses

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• 0:03 Acceptance Sampling
• 0:37 Acceptance Quality Level (AQL)
• 1:14 Operating Characteristic Curve
• 3:07 How to Use the Chart
• 3:56 Lesson Summary
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Lesson Transcript
Instructor: Martin Gibbs

Martin has 16 years experience in Human Resources Information Systems and has a PhD in Information Technology Management. He is an adjunct professor of computer science and computer programming.

Defects happen. How many are acceptable in a given lot of product? This lesson will define a quality control tool, the operating characteristic (OC) curve and provide examples of it in use.

## Acceptance Sampling

The goal in any production operation is to eliminate defects. However, as hard as we try to remove them, defects will happen. Since we know defects will occur, one of the questions we need to ask is: How much error can we accept? We know that even the best batter is going to strike out. What is the acceptable strikeout rate for a given batter? In order to evaluate our production lots or batches, we need to come up with a plan. Acceptance sampling is a means to evaluate lots to see if they pass the standard.

## Acceptable Quality Level (AQL)

Since we know that defects are unavoidable, we need to accept that certain batches or lots are going to have them. Buyers can accept a certain level of off-color paint or scuffed edges. The overall percentage is usually somewhere between 0.1 and 2%. This is the acceptable quality level (AQL). This number varies by product and defect. For a window manufacturer, discolored sills may have an AQL of 1.8%. Discolored glass, on the other hand, may have an AQL of 2% (or even higher). We'll see this number play into our diagram a little later.

## Operating Characteristic Curve

We can now take a graphical look at our sampling plan. It is important to see how well the plan truly picks out the good lots and discards the bad lots. An operating characteristic (OC) curve is a chart that displays the probability of acceptance versus percentage of defective items (or lots).

With no defects, we'll surely have 100% acceptance! But, take a look at 0.05 (5% defective). At this point, there is still 90% acceptance. Then, the curve starts dropping.

### The Curve

No sampling plan is going to be perfect. Good lots will get rejected, and bad ones will be accepted. There will be a pitcher who hits four home runs in a game and the star batter will whiff on every pitch. If we sample only a single game, it's difficult to trust the strength of our sample. However, if we run multiple samples we can have a richer set of data to work with.

As a rule, if the curve is steeper, it indicates a better sampling plan. Take a look at the following example. The curve is much steeper. We got this by increasing our sample size.

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