From: Stan Hilliard shilliard@samplingplans.com
Date: 19 Aug 2001
Time: 17:44:38
With non-normal variables, when you convert the acceptance criteria (AQL, RQL) from an Specification Limit (ISL) basis to an equivalent lot-mean basis, consider the lot by lot nature of the acceptance decisions. Sampling plans apply to product lots for decision - one lot at a time. So the calculation of the AQL-mean, the RQL-mean, and the (known) standard deviation should be based on within-lot data.
If raw data from multiple lots is combined into one group, a difference between lot means can make the data appear non-normal even though the within-lot variability follows the normal distribution.
Additionally, when raw data from a group of lots is combined, a difference between lot means will also cause the standard deviation to be larger than the actual within-lot standard deviation.
It is best to collect baseline data over multiple lots and then "pool" the lot data. Do this by subtracting, from each measurement (X), its own lot average (Xbar). Then combine the (X-Xbar) from all lots into one group.
Since each of these deviations from the lot mean is calculated within the same lot, you can combine the (X-Xbar) from multiple lots and still have within-lot data. This data provides the baseline to calculate the AQL-mean, the RQL-mean, and the within-lot "known" standard deviation. You will use the as input for the sampling plan for the mean.
Using this method, any difference between the means of the baseline lots will have no effect.
Stan Hilliard