AQL Based Sampling Plans

  • ANSI/ASQ Z1.4-1993 (MIL-STD 105E was withdrawn in February 1995) sampling plans are based on the use of AQL – the percent defective that is considered acceptable as a process average for the purposes of acceptance sampling.
  • With these plans, it is not necessary to assume the provision of 100% screening (with replacement of all defective units) of all rejected lots.
  • To enter any of these tables, you must first decide on the AQL to use (and determine the sample size code letter); from the table you will get the acceptance number (Ac) and the rejection number (Re) for the plan.
  • There are also separate tables to provide the AQL for different values of AQL and sample code letters


– More serious defects should have a lower AQL as the acceptance criterion, and less serious defects can have higher AQLs – using a Classification of Defects system.
– Tightened inspection should be used whenever the quality history is unsatisfactory or when there are other good reasons for being suspicious about quality – keeping the beta risk down.
– Reduced inspection can be used when the quality history is shown to be good enough through Normal inspection.
– These plans are generally chosen to protect the producer under normal conditions, i.e., not to reject submitted lots that are at the AQL or better when there are no reasons to be suspicious about quality.

Double Acceptance Sampling Plans


• There is usually less sampling than for a single sampling plan
• The OC curve is better than the c = 0 curve for the single sampling plan with a smaller R (for better discrimination)

Designing your own double acceptance sampling plan


Desired α risk of .05 for a P1 of .008, along with a desired risk of .10 for a P2 of .06. Use Table 4-4.
1. Determine R:

R = P2/P1 = .060/.008= 7.5

2. Enter Duncan’s Double Sampling Tables and find the closest R to the calculated value in step 1.
The closest table value is 7.54 in Plan Number 2. This is very close to 7.5. Note the c1 value of 1 and the c2 value of 2.

3. For Pa1-α = .95, obtain the nP1 (Pn1 in the table) value. Then calculate n from:

n = nP2/P2 = 0.52/0.008 = 65.

The acceptance sampling plan is n1 = 65, c1 = 1; n2 = 65, c2 = 2.

Variables Sampling Plans

ANSI/ASQ Z1.9 (MIL-STD-414 is withdrawn) sampling plans are based on the use of variable data (from an assumed normal distribution).

Actual measurements are made on the samples : the sample data is used to calculate a statistic, such as X̄, R, or S and then the calculated statistic is compared to the critical value from a table.

Acceptance criteria must be applied separately to each quality characteristic (vs. overall lot accept vs. reject for attribute sampling), so it’s more expensive than attribute sampling for larger lots, so it’s generally best to use only on key characteristics, with attribute sampling on the rest.

Compared to attribute plans, these plans, for the same n, provide a greater quality protection in judging a single quality characteristic, or for the same amount of risk, a smaller n is OK.

The use of variable data can provide more information about the extent of nonconformity – How? (Hint: think frequency distribution and what you can do with this information).

These sampling procedures are based on the assumption that the quality characteristic is normally distributed (it is possible to use data transformation if it is not). Procedure:

To use any of these plans, you must first decide on the:

  • Inspection level (II is the default for Z1.9)
  • Method to use – S or R, with variability (population sigma) known or unknown (see Decision Tree)
  • AQL
  • Lot size

Determine the sample-size code letter from the table

Calculate the Q value

Enter the Master Table by sample size code letter and AQL, and look up the k value.
Compare the k and Q values – if the calculated Q value is ? than the critical k value from the table, accept the lot. If not, reject it.

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