From: Stan Hilliard
Date: 19 Jul 2003
Time: 13:01:31
Chris,
Assuming Go, No-Go attributes test data:
How do you want to define your sampling requirement? That is, is there a maximum number of defective wheels that, if they exist, you want to be sure of rejecting?
I assume that you want to sample less than 1/10 of the lot. If so it is appropriate to use an attribute plan based on the binomial distribution. The oc curve that describes the ability of the sampling plan to detect would have fraction defective (or percent defective) on the horizontal axis.
www.samplingplans.com/usingoccurves.htm
You would be most interested in the right end of the oc curve. (Low probability of acceptance of the lot if the fraction defective is high.)
As an example, say that you want sampling plan that provides, if 10 wheels are defective in a lot of 100,000, only Pa=5% probability of acceptance.
The software program TP105 will allow you to, by trial and error, determine several sampling plans that meet that criterion. There will be a plan for each possible acceptance number (0, 1, 2, ... etc.) The plan with the smallest sample size will be for Ac=0.
You would do this by picking sample size=n, acceptance number=Ac combinations. For each (n,Ac) combination that you pick, the program TP105 calculates the fraction defective that will have Pa=5%. That fraction defective is labeled "RQL", meaning "Rejectable Quality Level".
Once you have the (n,Ac) of a fixed-n plan, TP105 can convert it to a sequential plan. Sequential sampling plans are the most efficient possible type of plan in terms of the smallest sample size to meet the probability that you specify -- the Pa=5% in this example.
An exception: My assertion that sequential sampling plans reduce the sample size is true for all plans except those with Ac=0. For fixed-n sampling plans with Ac=0, sequential plans cannot reduce the sample size further, but they can provide a "second chance" to meet the specified Pa=5% by increasing the sample size.
For example, if one defective wheel is found before reaching the n that allows acceptance if Ac=0, the fixed-n plan would reject, the sequential plan (properly designed) could allow you to choose to accept on Ac=1 if you increase the sample size sufficiently.
TP105 is described at:
www.samplingplans.com/programtp105.htm