Normally, companies use either the DS ISO 2859 series standards or the DS ISO 3951 series as a basis for sampling and approval of batches based on a given AQL value.

However, these two groups of standards are based on some general assumptions that must be met before the results work as intended. Firstly, it is a condition that any defective items are randomly distributed throughout the batch in question. This means that the systems do not work if there is an accumulation of failures in the batch (however, this is often seen).

The next condition is that the sample is taken randomly in the batch, so that each item has an equal probability of becoming part of the sample size indicated by the standards.

Of course, it is also a condition that the ability to distinguish between good and bad items should be tested and result found satisfactory by inspection of alternative (attributive) data using DS ISO 2859 series standards as well as the measurement uncertainty is appropriately small and the  characteristics are normal distributed using ISO 3951 series standards.

In practice, it has been found that companies use DS ISO 2859 part 1 and DS ISO 3951 part 1 almost exclusively respectively. For both standards, they only work in the case of so-called continuous batches. This means that this is a situation where a number of batches of goods come from the same production process over time.  The reason for this requirement is that an average error rate equal to the accepted AOQL value is only guaranteed if this is the case. However, experience shows that companies do not comply with these conditions and therefore have a much greater risk of receiving batches with far more errors than the AQL value conditions. At the same time, it is a requirement that batches that have more error items in the sample than the table values prescribe are sorted and all error items are removed.

There is no point in trying to take a new sample from repulsed batches of goods. In this way, the probability of approval increases regardless of the error content, which is why the agreed maximum error level cannot be guaranteed.

Example of using DS ISO 2851 -1:

We get batches consisting of 5,000 items from a supplier. The supplier must deliver goods with an AQL value equal to or better than AQL 0.4.

We take samples from the batches with the following results from a sample established in the standard for 200 items.

10 samples each of the size 200 pieces

Before rebuttal, Error 0,36% <0,65<1,11

After rebuttal,Error0,27% <0,56<1,10

This means that with such a sample, we can risk up to 1% defects in the goods. The standard says that we can risk approving a batch of goods with up to 2.6% error items.

There is another standard DS ISO 2851 part 2, which applies to individual batches or batches of goods that are resubmitted after sorting. The rejected batch in this case is not part of a continuous delivery, which is why 2859 – 2 must be used.

If the 5,000 items come from a single batch of goods, the sample size must be 315 pieces and there must be no errors.


Example of using DS ISO 3951 – 1

We may use this standard instead if there is only one property that needs to be inspected. Of course, it can also be used for each property in a subject with several important properties.

Same item as above with 5000 items in each delivery. Now the sample size should be 61 items and a k-value of 2,230.

If our property is a length of 20mm and with a tolerance of +/- 0.05 mm, the result may look like this:

Sample size 61, average 20.021 mm and a standard deviation of 0.0112 mm

ØTG-X(bar) /s =0.029 /0.0112 =2.589 greater than 2.230 -> approved with an error rate of 0.5

Problem with non-normal distributed properties

ØTG =920 μm and NTG= 550 μm

Sample size 61, average 718.3 mm and a standard deviation of 0.0112 mm

X(bar)-NTG /s =168.5 /61.03 =2,758 greater than 2,230 -> approved with 2 error items and an error rate of 1.2%

The batch should have been refuted with too many faulty issues.


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