From: Stan Hilliard
Date: 12/9/2005
Time: 12:34:06 PM
Lot size only effects the statistical calculations to a perceptible degree for sampling plans that sample more than 10% of the lot. For those plans, the accurate statistical calculation involves the hypergeometric distribution. That is complex so most so it is common to use the method that you mention.
I have found that there is very little reduction in sample size by using the hypergeometric. I plan to eventually add a lot size adjustment to TP105 based on an approximation to the hypergeometric.
There is a new windows version 3 of TP105 for attributes. It is not described on this website yet because the user manual is not ready. However, the [Help] system is very good and serves as a user manual. I am currently selling V3 for the same price as the old version. ($245)
The new V3 contains a C=0 tool that needs only the consumer's point as input.(RQL,Beta). RQL can be in units of fraction defective or Defective Parts Per Million (DPPM). The AQL is calculated at for Alpha=0.05.
Here is a possible solution to your problem. If your data is numerical measurements, V3 will convert a C=0 (or any other attribute plan) to a matching variables plan having the same producer's and consumers' points on the oc curve. Instead of (n,Ac) the decision rule has (n,k) , where k=3*Cpk of the lot.
Here is just one example of the gain for switching from attributes to a matched variables plan.
For n=200, C=0 ---> n=32, k=2.84, (SD unknown)
For n=200, C=0 ---> n=7, k=2.84, (SD known)
For n=200, C=0 ---> ASN=3.3 (sequential variables plan when the lot is AQL quality.
As you can see, when the data is a measured variable, there are tremendous efficiencies and savings to be realized by switching to a matched variables plan. This applies to any attribute plan, not just C=0 plans. And this often solves the "small lot" problem.