INTRODUCTION -- We advise purchasing agents to exercise caution if they specify an AQL based standard acceptance sampling plan for use with a purchase. Acceptance sampling has as its purpose to prevent delivery of an off-quality lot -- should it unfortunately be manufactured in the first place. When the purchaser specifies the AQL for an AQL based standard acceptance sampling plan with the belief that AQL protects them, he or she is mistaken. This is explained below.

The term AQL has two meanings.
 
(1) STATISTICAL MEANING OF AQL: -- Statistically, AQL is a quality level on the x-axis of an operating characteristic curve (oc curve).

AQL is the x-coordinate of the producer's point. For the example above, AQL=0.018. Also, for this example, the probability of acceptance at the producer's point is Pa=0.95.

Note that the oc curve also contains a consumer's point which designates the quality that would NOT pass the sampling plan. The quality level at the consumer's point is RQL (Rejectable Quality Level). For the example above, RQL=0.093. Also, for this example, the probability of acceptance at the consumer's point is Pa=0.05.
 
(2) MIL-STANDARD AND Z1.4 MEANING OF AQL: -- These standards instruct that AQL is the quality level to be specified by the consumer... (See sec. 4.3 of Z1.4.)
 
THIS IS A CONTRADICTION: -- The statistical definition of AQL associates it with the producer's point and the need of the producer to accept lots that have been manufactured to the AQL level, while the Military and Z-Standard instructions call for the consumer to specify AQL. The contradictory meanings of AQL arise because the Military and Z-standards are not organized according to the producer-consumer model.
 
SOURCE OF CONFUSION: -- No wonder so many people are confused - the Military and Z-standards reverse the meaning of producer and consumer. No wonder many purchasing agents wrongly believe that by specifying AQL they are enhancing their (consumer's) need to not accept off-quality lots.
 
The practical consequence of all this is that if you study Mil-Std-105E or ASQC/ANSI-Z1.4 to learn about AQL, you will learn a system, but you will also be learning how to specify sampling plans that are not designed to protect the consumer's interest.
 
MODERN ACCEPTANCE SAMPLING: -- In order for an acceptance sampling plan to be statistically valid, the person that specifies the plan must know and accept the probabilities and risks of that plan. You can learn about this  methodology to protect both the consumer and the producer by reading and printing the 20-page tutorial on modern acceptance sampling.
 
A shorter explanation of the correct way to develop an acceptance sampling plan explains the operating characteristic (oc) curve.
 
SOFTWARE FOR ACCEPTANCE SAMPLING: -- Modern acceptance sampling practice is supported by  acceptance sampling software that uses both the consumer's point and the producer's point of the oc-curve.

DISCUSSION FORUM -- You can collaborate with others to get additional questions discussed at the sampling plan forum .
 
Author --  Stan Hilliard, CQE,CRE,CQA,PE
shilliard@samplingplans.com