Attribute acceptance sampling plans are used when the assessment of the samples is either a binomial judgment of pass/fail or a Poisson count of defects. We will want to generate a figure for the number of items that should be sampled in order to decide if a lot can be considered acceptable or not. The amount of items that need to be inspected will be based on the amount of defects or defective items that we can accept and the amount that we would reject in a lot.
Defective items can be specified as percent, proportion, or defectives per million. Defects can be specified as per unit, per hundred, or per million.
AQL and RQL are used here to define the acceptable quality level and the rejectable quality level. Here, we will use the same AQL, RQL, and lot number as in the Creating an acceptance sampling plan for variable data recipe. This will highlight the difference in the sample sizes between variable and attribute plans.
The response will be used as a binomial, samples being good or rejected, to create a sampling plan. We will identify the number of samples that need to be inspected from each lot in order to decide if the lot can be accepted.
A lot is judged on the percentage defective product; we will want to accept lots with less than 0.1 percent defective and reject lots with more than 1 percent defective. The total lot size being judged is 5000 items.
There is no datasheet to open for this recipe. We will use an AQL of 0.1 percent with an RQL of 1 percent.
The following steps will create an acceptance sampling plan for an AQL of 0.1 percent and an RQL of 1 percent with a total lot size of 5000 items. The producer's risk will be set at 0.05 percent and that of the consumers at 0.1 percent.
- Navigate to Stat | Quality tools and select Acceptance Sampling by Attributes.
- Use the drop-down menu to select Create a Sampling Plan.
- Measurement type needs to be set to Go/no go (defective) for binomial data.
- Set Units for quality levels as Percent defective.
- Set the AQL to
0.1. - Set the RQL to
1. - Enter
5000as the Lot size. - Click on OK.
The results will indicate that we need to sample 531 items from a lot. A lot is acceptable if we observe two or fewer defective items from the sample.
This figure is much larger than the equivalent sampling plan by variables in the previous recipe. With attribute data, we lose information about the position that is collected with the variable data, and as such, this information is made up with more samples.
The acceptance plan that we have generated used binomial distribution to create the sampling plan. Our assumption is that the lot we are sampling comes from an ongoing process. The total number of items is very large. Occasionally, we may have a lot size that is finite, a one-off shipment, or product that is unique to each order. In these cases, we should select the hypergeometric distribution and not the binomial distribution. This is found from Options within the Acceptance Sampling by Attributes dialog box.
Another issue that arises here is the idea of an AQL and an RQL. The closer the two numbers, the more difficult it is to distinguish between them. To identify a result at 0.1 percent defective and a lot at 0.5 percent defective, we would need 1335 samples. To know definitively if a result is at 0.1 percent or is just above 0.1 percent, we would need to measure everything in the lot.
Often, acceptance plans that talk about an acceptance number of zero are discussed. These are known as C= 0 plans and are commonly used as a check for outgoing lots of pharmaceutical products. These plans also use only one quality level, and this can cause confusion over the use of AQL and RQL. C = 0 plans are more commonly associated with one quality level. This is usually the RQL, although it can be referred to as the AQL, or rather, the Lot Tolerance Percent Defective (LTPD). For acceptance plans that only accept on zero defective items, see the next recipe.