## Z 1.4 AQL Levels Question

I need help understanding the AQL values in the tables of ASQ Z1.4. They are defined in paragraph 4.5 as percentages or ratios, but there are some values that are less than 1 and greater than 100. How should these values be interpreted?  Since this standard is for attribute data, is there a standard for variable data?

A percentage can be from 0 to more than 100% depending on what the ratio represents.  First we need to define AQL.  Section 4.2 states “The AQL is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.”  Therefore, an AQL of 0.65% means that on average we can accept 65 defects per 10,000 units in a lot.  The sampling plans with percentages greater than 100% are carried over from the MIL-STD-105 and are considered to be antiquated and not used any longer.

The ANSI standard for variable data sampling plans is ANSI/ASQ Z1.9.  It is based on probability of being outside the acceptance region.

Steven Walfish

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## Z1.4:2008, Using Acceptance Quality Limit (AQL) Q: I have a question about how to use ANSI/ASQ Z1.4-2008 Sampling Procedures and Tables for Inspection by Attributes.

I am looking to achieve a 99.5% production yield.  How do I calculate that using the Acceptance Quality Limit (AQL) in this standard?  Is it as simple as taking (100-AQL) to calculate the expected yield?

A: The ANSI Z1.4-2008 standard is not intended for calculating production yield or expected production yield.  The AQL is the maximum percent non-conforming that can be considered acceptable as a process average.  Typically we set this as the percent defective that would be accepted at a 95% confidence.  If you want to sample such that you have 95% confidence that the average production yield is 99.5%, you can find a sampling plan with an AQL of 0.5%.  Also, please understand that the tables in the standard are not exact value for AQL.  Using the binomial distribution (or hypergeometric for sampling with no replacement) you can calculate the exact probability.

Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
ASQ CQE
Statistician, GE Healthcare
http://statisticaloutsourcingservices.com/