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 ISO 3951-1 is the first in a series of international standards that applies statistical methods to checking product quality, and has now been updated. This blog post looks behind the scenes at how the standard works and at what’s changed.

Sampling procedures for inspection by variables — Part 1: Specification for single sampling plans indexed by acceptance quality limit (AQL) for lot-by-lot inspection for a single quality characteristic and a single AQL  is a long name for a straightforward international standard. It’s about sampling products to check their quality against a single quality characteristic.

Single sampling plans

To be specific, ISO 3951-1:2022 specifies single sampling plans for lot-by-lot inspection under certain conditions. These are where the inspection procedure is applied to a continuing series of lots of discrete products all supplied by one producer using one production process, and where only a single quality characteristic, x, of these products is taken into consideration, which must be measurable on a continuous scale.

The standard should also only be deployed where production is stable (under statistical control) and the quality characteristic, x, is distributed according to a normal distribution or a close approximation to the normal distribution.

Finally, it should only be applied where a contract or standard defines an upper specification limit U, a lower specification limit L, or both. An item is qualified as conforming if and only if its measured quality characteristic x satisfies the most appropriate of the following: x is greater than or equal to L; x is less than or equal to U (both called cases with a single specification limit); or x is greater than or equal to L and less than or equal to U (called cases with a double specification limit).

Where double specification limits apply, it’s assumed in ISO 3951-1:2022 that conformity to both specification limits is equally important to the integrity of the product. In such cases, it’s appropriate to apply a single AQL to the combined percentage of a product outside the two specification limits. This is referred to as combined control.

Probability of acceptance

In ISO 3951-1:2022, the acceptance of a lot is implicitly determined from an estimate of the percentage of nonconforming items in the process, based on a random sample of items from the lot.

The idea is that the standard is applied to a single quality characteristic that is measurable on a continuous scale and is normally distributed. For two or more such quality characteristics, see the next standard in the series, BS ISO 3951-2. Note that the procedures in Part 1 are not suitable for lots that have been screened for nonconforming items.

Notwithstanding all of the above, the overweening objective of the standard is to pragmatically ensure that lots of acceptable quality have a high probability of acceptance, while the probability of not accepting inferior lots is as high as practicable.

This is achieved using the switching rules that tighten or discontinue sampling inspection when a deterioration in quality is detected; and conversely, and at the discretion of the responsible authority, switches to a smaller sample size (reducing inspection costs) if consistently good quality is achieved. ISO 3951-1:2022 thus enables users to improve sampling efficiency and reduce risk simultaneously.

Technical changes

ISO 3951-1:2022 is an update to the 2013 version of this standard. The two key changes are that procedures have been introduced to accommodate measurement uncertainty and many of the sampling plans have been adjusted to improve the match between their operating characteristic curves and the operating characteristic curves of the corresponding plans for single sampling by attributes in BS ISO 2859-1.

In addition, long-term users will notice major changes to the standard’s layout, with many of the tables and diagrams having been removed. And in an effort to streamline and modernize the document, software has now been introduced that supports the implementation of the acceptance tests and also produces information that was previously found in the old standard’s tables and diagrams. The software is informative and therefore not a requirement as such. However, you won’t be able to use the standard fully without it so the recommendation is that you download and use the software provided.