Steve,
Excuse my overly analytical nature haha, I have found the reference but it seems that I have somewhat misinterpreted what it implies:
"Type-A and Type-B OC Curves. The OC curves that were constructed in the previous examples [irrelevant here] are called type-B OC curves. In the construction of the OC curve it was assumed that the samples came from a large lot or that we were sampling from a stream of
lots selected at random from a process. In this situation, the binomial distribution is the exact probability distribution for calculating the probability of lot acceptance. Such an OC curve is referred to as a type-B OC curve.
The type-A OC curve is used to calculate probabilities of acceptance for an isolated lot of finite size. Suppose that the lot size is N, the sample size is n, and the acceptance number is c. The exact sampling distribution of the number of defective items in the sample is the hypergeometric distribution.
Figure 15.6 shows the type-A OC curve for a single-sampling plan with n = 50, c = 1, where the lot size is N = 500. The probabilities of acceptance defining the OC curve were calculated using the hypergeometric distribution. Also shown on this graph is the type-A OC curve for N = 2000, n = 50, and c = 1. Note that the two OC curves are very similar.
Generally, as the size of the lot increases, the lot size has a decreasing impact on the OC curve. In fact, if the lot size is at least 10 times the sample size (n/N ≤ 0.10), the type-A and type-B OC curves are virtually indistinguishable."
Douglas C. Montgomery, Introduction to Statistical Quality Control, 6th Edition.
Now, based on rereading this in this context, I would assume the following (please confirm):
1.) Sample size is irrelevant to lot size. Based on AQL, RQL, alpha, and beta, I can use the binomial/Larson nomogram (for single plans) or ANSI Z1.4 tables to get n & c.
2.) After I get n & c, I compare n to N. If the condition is satisfied, I calculate the probabilities of acceptance using the binomial formula. If not, then I calculate the probabilities of acceptance using the hypergeometric formula (which I have for acceptance probabilities), so no issue here if this is the case (for now at least!).
Issue here: If I use the nomogram for my case, I get n=120, c=3. This does not satisfy the binomial approximation condition, and therefore when plotting the OC curve I would use the hypergeometric formula to calculate probabilities. However, if I use ANSI Z1.4 tables, I might (probably will) get a different n and c values than from the nomogram. Now, what if the n value from the ANSI tables satisfies the binomial condition? (For example, say I get an n=80 from the tables). This would satisfy the condition if my lot size is 821 units, and I would therefore be able to use the binomial to plot the OC curve. Won't this make a difference in my OC curve? Which would be safer to go with (more accurate)?
3.) If the sample size obtained is larger than the lot size, do 100% inspection.
Do I make more sense now? I hope this is correct, because if it is, then I'm sorted for single plans.
However, I am also required to develop a double sampling plan to compare. It would seem to me that for double sampling plans, the nomograph cannot be used. However, from some reading it seems that the (beta/alpha) tables are what is used in this case to get n & c. I have a few questions here.
1- Are there any other standards/systems one can use to develop a double sampling plan other than the beta/alpha tables?
2- Since there will be 2 samples sizes in this case (n1 & n2), what would be the criteria to determine whether the OC curve should be based on the binomial or hypergeometric?
Please keep the discussion going!