From: Stan Hilliard shilliard@samplingplans.com
Date: 17 Aug 2001
Time: 11:07:54
Greetings Khalil, I can think of two solutions for when the distribution of individuals is not normal:
Solution A) You can use a sampling plan for the mean and specify AQL-mean RQL-mean directly. Plans for the mean do not require a normal population because of the Central Limit theorem. The Central Limit theorem says that the distribution of sample averages will be normal even if the distribution of individual measurements in the population is not normal. This is sufficient to make the sampling plan work accurately for sample sizes of 4 and above.
Solution B) The second situation is when you cannot specify the AQL-mean and RQL-mean directly because your criteria are based on conformance to specification limits for individuals (ISLs).
In this case you need to start with the AQL-fraction defective and RQL-fraction defective and then calculate the AQL-mean and RQL-mean from them. You can't use the normal distribution for this calculation because the population is not normal.
Use your non-normal within-lot data. Tabulate and plot the cumulative histogram. With this, determine the distance from ISL to the AQL-mean that will result in AQL fraction defective beyond ISL. You can use normal probability graph paper for this. Repeat this procedure for RQL fraction defective to determine the RQL-mean.
If you have both lower ISL and upper ISL, calculate a set of AQL-mean & RQL-mean for each ISL.
As you can see, solution (A) above is the simpler of the two methods.
To summarize, I would use a sampling plan for the mean when it is necessary to account for a non-normal distribution of individuals. Sampling plans for the mean do not assume that the population is normally distributed.
Sincerely, Stan Hilliard