# Acceptable Quality Level (AQL)

The number of allowable defects in a batch

## What is the Acceptable Quality Level (AQL)?

The Acceptable Quality Level (AQL) is a quality control concept. It is the minimum level of faults acceptable in a sample of a manufactured product for the entire batch of the product to be accepted. If the number of faults is higher than the AQL, then the entire batch is rejected. ### Sampling Process

The process of sampling requires that some preliminary parameters be fixed, including the AQL that would feed into the final decision about accepting or rejecting a batch of product. The parameters are:

#### 1. Inspection Level

The three levels of inspection levels are normal, tightened, and reduced. Usually, the normal level is used to assess samples for faults. The level depends on the performance of the supplier. Consistently poor performance leads to tightened inspection, which is a stricter process. A good track record, on the other hand, leads to a reduced inspection level.

#### 2. Acceptable Quality Level

The acceptable quality level is the number of allowable defects in a batch. The AQL is agreed upon between the buyer and the supplier based on the importance of the product. For example, the AQL for a batch of t-shirts can be 1 per 1,000, whereas, for a batch of mobile phone batteries, it is much lower, like 0.001 per 1,000 or 1 per 1,000,000 faults.

#### 3. Sampling Method

A few sampling methods can be used to achieve quality assurance based on the level of sophistication and rigor required. The key methods are as follows:

Single sampling is the most common method. It only requires one sample of size n and the number of defaults c. Hence, it is also called (n,c)-sampling. If in the sample of n defaults are greater than c, the entire batch is rejected.

Double sampling is an extension of the single sampling method. In such a case, if the first sample is indecisive, then a second sample is taken to make the decision.

Sequential sampling is an elaborate method where each item from the sample is tested, and a decision to accept, reject, or continue testing is made after every item is tested.

The other methods are multiple sampling and skip lot sampling.

### Connecting Acceptable Quality Level to Sampling

Before connecting all the dots, a few more concepts need to be understood. The concepts are:

#### Producer’s Risk

It is the probability that in an (n,c)-sample the number of defaults is greater than or equal to the AQL. Hence, it is the probability that the lot is rejected. It is typically denoted by the Greek letter α (alpha).

#### OC Curve

The Operating Characteristic Curve (OC Curve) plots the percent of defaults or AQL (x-axis) for a single or (n,c)-sample against the probability of accepting a batch (y-axis). The curve is illustrated below. As the curve shows, as the number of faults rises, the probability of acceptance falls rapidly.

For those with knowledge of statistics, the OC Curve shows a familiar shape – it is the survival function. Thus, the points on the curve can be thought of as the probability of a batch surviving (being accepted) given the percentage of defaults for a given sampling method. ### The Connection

When designing a sampling process, a manufacturer or producer wants to minimize the probability of rejection – that is, they wish to minimize α as defined above. It is the same as maximizing (1-α) or the probability of acceptance for a given sampling method.

The producer chooses the AQL using the OC Curve in conjunction with their knowledge about other factors like the quality of machines and workers involved in the process, quality of raw materials, the quality demanded by customers, and any other factors that affect quality.

For example, assume the stated sampling method is a single sample (60, 4) with the size of 60 and a rejection level c equal to 4. If the producer sets their AQL to 5% (3 per 60), the probability of the sample being accepted is around 80%. At this stage, if the producer thinks it is too risky, they can make the necessary changes so that the AQL is 2% (1.2 per 60). It yields the probability of acceptance of about 99% based on the OC curve above.

The OC Curve can also be used to choose a sampling method. The producer can pick the sampling method that maximizes the probability of acceptance for a given AQL.

Let’s say a producer realizes there is no way they can reduce the number of defects below 5%. Now, if they were using the above (60, 4) sampling method, their probability of rejection would be 20%, as given by the OC curve, which is very high. To overcome the issue, they can use a different sampling method by plotting different curves and picking one that is acceptable to them as well as their customers. For example, in the figure below, the producers can negotiate using (80, 6) instead of (60, 4) to increase the probability of accepting to 90%. ### AQL in Practice

The above examples discuss only one sampling method – the single sampling method. In practice, the computations would be more complex than the ones illustrated above. To make the task of implementing quality standards simpler, AQL charts are used.

The number of acceptable faults in a sample – depending on the batch size, inspection level, and the AQL – can be easily read off the charts. The chart provides thresholds for acceptance and rejection of a batch, which can be used to make the final decision.

### Using AQL Charts

The AQL chart comprises two parts – the first one is the inspection level chart. It is used to choose the inspection level based on the batch size and the level of scrutiny that is required. For example, assume a batch of 5,000 shirts needs to be stitched, and the level of inspection is set at Normal II. The level of inspection, according to the prescribed table, is at the intersection of the batch size row and inspection level column. As shown in the table below, it is inspection level “L.” The next step in the process is to determine the appropriate sample size, pick the AQL, and make a decision based on thresholds given by the chart. The thresholds are determined similarly at the intersection of inspection level row and AQL column.

Since the manufacturer is performing a normal inspection, we pick the normal table. Note there are different tables for tightened and reduced sampling. Assuming the AQL to be 4 per 1000 pieces, we get that the sample size should be 200 shirts. If there are 15 or more defective shirts, the manufacturer should reject the entire batch. 