A previous blog,AQL (Acceptable Quality Level) sampling can be deceptive, described issues with AQL testing. This blog will elaborate more on this point using an example.
For N (lot size) = 75 and AQL = 4.0%, ANSI/ASQC Z1.4-1993 (Cancelled MIL-STD-105) yields for a general inspection level II a test plan in which:
From this plan we can see how AQL sampling protects the producer. The failure rate at the acceptance number is 7.6% [i.e., (1/13)(100) = 7.6%], while the failure rate at the rejection number is 15.4% [i.e., (2/13)(100) = 15.4%].
Usually a sample size is considered small relative to the population size if the sample is less than 10% of the population size. In this case, the population size is 75 and the sample size is 13; i.e., 13 is greater than 10% of the population size. However, for the sake of illustration, let’s determine the confidence interval for the failure rate for the above two scenarios as though the sample size relative to population size were small. This calculation yielded:
Test and Confidence Interval for One Proportion
Test of p = 0.04 vs p < 0.0495% Upper Exact
Sample X N Sample p Bound P-Value
1 1 13 0.076923 0.316340 0.907
Test and Confidence Interval for One Proportion
Test of p = 0.04 vs p < 0.0495% Upper Exact
Sample X N Sample p Bound P-Value
1 2 13 0.153846 0.410099 0.986
For this AQL test of 4%, the 95% confidence bound for one failure is 31.6% and for two failures is 41.0%. Practitioners often don’t realize how these AQL assessments do not protect the customer as much as they might think.
This example illustrates how a test’s uncertainty can be very large when determining if a lot is satisfactory or not. A lot sample size to adequately test the low failure rate criteria in today’s products is often unrealistic and cost prohibitive. To make matters worse, these large sample sizes would be needed for each test lot.
In the next few blogs, I will describe an alternative methodology that not only overcomes the above AQL issues but also addresses other corporate scorecard issues. In addition, this metric can provide predictive statements throughout organizations.
