AQL Calculation Explanation

Reporting, best practices, non-compliance reporting


Regarding part of your answer to a post found here, you state:

“The calculation of AQL is not dependent on lot size. In other words, a sample size of 315 gives a minimum AQL of 0.04, so a larger sample is required to estimate an AQL of 0.01.”

Can you explain for the non-statistical folks like me people how that math works? Specifically, I am wondering what the minimum sample size would be for an AQL of 0.25, when using Special Inspection level S2? Would it be a minimum of 50, no mater what the lot size is?


Acceptance sampling procedures were developed during the early 1920s at Western Electric Company and later formalized at Bell Telephone Laboratories where terms like producer’s risk and consumer’s risk were established.  Later, during World War II, sampling plans such as MIL-STD-105 were developed by Harold F. Dodge and others working with the Army Quartermaster Corps (Dodge, 1967).

Two special features were employed in order to gain agreement with the large body of military suppliers.  One was the use of the acceptable quality limit (AQL) as opposed to the RQL in presenting the plans.  The goal at the time was to focus on rewarding suppliers for production whose quality levels were considered good.  RQLs were recognized but not often brought to the surface during discussions. Also, at that time, the term “AQL” was deliberately vague or inexact.  It was a close approximation, not an exact probability statement.

The other feature was the practice of increasing sample sizes with increased lot sizes.  As noted in Section 3, in most situations, the lot size does not factor in plan construction (based on the binomial).  For many, however, this lacks intuitive appeal.  Therefore, in the development of MIL-STD-105 and its derivatives a deliberate increase in sample sizes for higher lot sizes was introduced, with corresponding increases in acceptance numbers for similar AQLs.  Clearly, this practice resulted in over-sampling and consequent increased inspection costs.  Government operatives believed that the increased sampling cost was of small consequence relative to the power to persuade.

For the binomial distribution you solve for the AQL that gives a high probability of passing.  Usually this probability is set at 95%.  For example if you have a sample size of 80 units with an accept/reject of 1, an AQL of 0.65% would have a 90% probability of passing the sampling plan.

You can use Excel to solve this with the function


Hope this helps,

Steven Walfish

Click here for more about these inspection standards.

Sampling Plan Review?

Chart, graph, sampling, plan, calculation, z1.4


When following ANSI/ASQ Z1.4-2003 (R2018), if a product has been placed in a “reduced” sampling plan based on the previous 10 lots results, is it a requirement to convert back to a “normal” sampling plan on an annual basis, or should that decision remain based on supplier performance? I have been told that we should revert to normal sampling each year, but I do not see that in the AQL inspection manual.


The standard does not require annual (or periodic) review of the sampling plan.  The switching rules are time invariant, and reflects just the normal flow of lots, which can span more than a year.  Unless the supplier requires a change in the inspection level, the standard is silent on resetting to the normal level annually.

Steven Walfish

Click here for more on these standards. AS9100 D

Airplane, aerospace, AS9100


Section of AS9100D States that “the organization shall establish, implement, and maintain a process for the recall of monitoring and measuring equipment requiring calibration or verification.”

Are calibration and verification both referring to the checking of equipment to make sure that it is suitable for it’s purpose, or is verification referring to the measurements taken on product? More specifically, does this require the organization to be able to identify which piece of measurement equipment made which measurements? In other words, if I have two micrometers that are both in a system that recalls them periodically for calibration, have I satisfied the requirements of even if I don’t record which micrometer makes which measurements during it’s daily use?


The calibration or verification both refer to the monitoring and measurement equipment.  The AS9100D additional text is consistent with the ISO 9001:2015 by referring to calibration or verification.  The monitoring and measurement equipment could require verification as meeting requirements instead of a calibration.  If monitoring and measurement equipment is found to be out-of-tolerance and there is a product conformity impact, then it is very helpful if the organization has identified which instrument was used for which job.  Otherwise, the recall of product or alerting customers is much broader since the impact is not understood.  There is not specifically an AS9100D requirement to record which monitoring and measuring equipment was used but it is a good practice.

Buddy Cressionnie

To learn more about this topic, visit ASQ’s website.

Z 1.4 AQL Levels

Food safety testing, lab, standards


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

Looking for the latest copy of the Z standards?  They are available here.