From: Stan Hilliard
Date: 23 Mar 2001
Time: 14:21:52
Hi Paul,
You said: "Should I review the procedure and create my own statistically valid sampling plan?"
I would say yes, because statistically validity means to know the probabilities of accepting lots having various quality levels. Generate the OC curve(s) for the plan. You will have a different oc curve for different sample sizes.
www.samplingplans.com/usingoccurves.htm
Additional considerations: Is the current plan an attribute plan or a variables plan? If attributes, should a variables plan for the mean be used instead? See: www.samplingplans.com/outputvariablesmean.htm. An attribute plan might not be discriminatory enough for small lots.
Do the drums come from a homogeneous lot? What are the sources of variability? To answer this, compare standard deviations calculated in three different ways: 1) on repeated tests of the same sample, 2) on multiple samples within a drum, and 3) on multiple drums - one test per drum.
I have seen a square root rule used to distribute a pre-determined sample size of items among packages - when there are multiple items in each package. It determined how many packages to open. Then multiple items were selected per package. This approach was used when it was too difficult to take a purely random sample of items - it does not have any statistical basis. It was a substitute for random sampling - not for sample size determination.
The only problem that I see with this method of selecting a random sample is that if the level of the quality characteristic is clustered within packages then the difference between packages will be under-sampled. In this application the sample size of items was determined prior to using the square root rule - not to determine the number of items.
My advice is to have a sample size of tests independent of lot size - based on the oc curve probabilities that you need. You could use a square root rule to distribute the tests among drums providing drum-to-drum variability is not greater than test variability. The lots for which the disposition is made should be "natural lots" of the manufacturing process.
Stan Hilliard