Acceptable Quality Level

Talk of acceptance and rejection of a sampling lot, based on an objective Yes/No assessment and we are talking of Acceptable Quality Level (AQL), also known as Assured Quality Level or Allowable Quality Level. By the books though, I will stick to Acceptable Quality Level, also popularly known as AQL in the remainder of this read.

AQL translates to level of quality, which is defined by percent defective, defects per hundred units or defective rate. It is that level of quality at which the sampling plan can be passed or accepted, 95% of the time. If the lot inspected fails the sampling plan, you can with 95% confidence say that the sample contains defective items and all the items need re-checking before sending to the customer.

As per Standard Military Sampling Procedures (MIL-STD), which have been used for a long time now to achieve these goals, AQL is defined as the maximum percent defective that for sampling purposes, can be considered satisfactory as process average.

AQL is the acceptance level, which means the probability of acceptance of the lot must be high for the lot to be passed. When used in Quality Control, the process is said to be at an acceptable quality level if the control chart doesn’t fall outside the bounds of the Control Limits.

In simple words, AQL is an inspection standard that describes the maximum number of defects allowed or acceptable in random sampling of an inspection. If the lot AQL is more than the AQL desired or allowable levels, the lot has to be rejected and cannot be shipped to the customer.

To understand the AQL Levels, a technique known as Acceptance Sampling is used. This sampling technique acquired popularity during World War II, exactly the place which formalized MIL-STD105. Acceptance sampling may not be widely used in industries what with most companies moving to a more robust DPMO/PPM calculation, it must be said that some companies still work on the AQL metric.

The AQL in acceptance sampling is the average percent defect level for a given process that has a 95% or greater chance of being "accepted" by sampling plan as characterized by the Operating Characteristic Curve (O-C or the Beta curve) for the sampling plan.

Acceptance sampling inspection is a formal hypothesis test. The O-C curve describes the level of protection provided by a particular sampling plan against "rejecting" good lots of product (producer's risk) having a proportion of defective units less than the AQL, or "passing" bad lots of product (consumer's risk) having a proportion of defective units greater than either the RQL (Rejectable Quality Level) or LTPD (Lot Tolerance Percent Defective). When one conducts acceptance sampling and passes inspection the confidence claim with reference to the AQL is as follows:

I have a (1-beta) confidence (really Power) that the defective rate is not greater than the AQL.

For example, suppose I develop a sampling plan consisting of n=50 samples and an accept number of a=1. This was considered a Level H sampling plan with an AQL=1% by the now obsolete MIL STD 105E Sampling Procedures by Attributes. The AQL (the 95th percentile of the O-C curve) for this sampling plan is equal to 0.72% defective, and the Lot Tolerance Percent Defective (LTPD, is the 10th percentile of the O-C curve) is 7.6%. It is never appropriate to characterize a sampling plan by only one parameter such as the AQL. Instead, a properly characterized sampling plan lists both the acceptance and rejection criteria via its O-C curve. The probability and confidence claims I can make for this sampling plan (n=50, and a=1) is:

Probability Claims: This plan will accept lots having an average defective rate of <=0.72% about 95%(beta%) of the time. The plan will reject lots having an average defective rate of >=7.6% about 90%(1-beta%) of the time.

Confidence Claims: For lots having an average defective rate of <=0.72% the acceptance confidence claim is: I am <=5%(1-beta%) confident the defective rate is less than or equal to 0.72%. For lots having an average defective rate of 7.6%, the rejection confidence claim is: I am 90% confident the defective rate is greater than or equal to 7.6%. Between the defect rates of 0.72% and 7.6% the sampling plan will accept or reject lots based on the results of the inspection. The region on the O-C curve between the AQL and the LTPD is called the Indifference Quality (IQ) region.

In 1995 MIL STD 105 was obsoleted by the US government, and a reasonable replacement is ANSI/ASQ Z1.4 for attributes sampling.

In 1999 MIL STD 414 was obsoleted by the US government, and a reasonable replacement is ANSI/ASQ Z1.9 for variables sampling.

The uses of acceptance sampling are:

  1. To guard against the release of poorer quality lots, when lot quality is unknown.
  2. To improve customer value when lot quality is highly variable.
  3. To detect major process failure, and set the stage for quality action.
  4. To reject obviously bad lots, or when samples are required for other purposes like SPC.

When to discontinue acceptance sampling inspection:

1) When the process consistently produces a low level of defects,


2) When the process is fully mistake proofed,


3) When sample are not required for other purposes such as process control, tracking the process average, etc.

MIL STDs 105 and 414 were developed to support military NOT industrial applications. As such, within these MIL STDs as the lot size increases the size of the sample for inspection increases. This approach scales the sampling plan to the lot size which is not statistically valid. If you desire a fixed level of protection, which is provided by a sampling plan, then changing the sampling plan size changes the protection.

Other terms associated with AQL are RQL (Rejectable Quality Level) and Average Outgoing Quality Limit (AOQL). A lot having high AQL has a high amount of non-conformities. Reworking on these non-conformities is added cost to the company, which it should look at saving. Thus, companies look to build quality checks with the process rather than just having an inspection at the end of the process.

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