From: Stan Hilliard
Date: 11/27/2005
Time: 10:45:49 PM
Hi Stan,
You have two sampling plans in series -- as you correctly describe. To describe them in my own words:
1) CONTAINER PLAN - The first plan (second mentioned) decides to accept/reject a container. Its oc curve is calculated from n=13 units, Ac=0 defective units, Re=1 defective unit. The X-axis of that oc curve is the true process fraction defective units. The Y-axis (Pa) of that oc curve is the probability of accepting a container. Equivalently, (1-Pa) is the fraction of containers that will be determined to be defective.
2) LOT PLAN - The second plan of the series is the plan that decides to accept/reject the lot based on rejected containers. n=50 containers, Ac=1 rejected container, Re=2 rejected containers.
3) COMPOSITE PLAN: In order to calculate a point on the oc curve of the two decision rules combined in series, you first need to, for each p' fraction defective of product, calculate the Pa of the container plan. Then use that (1-Pa) as the p" of the lot plan to calculate the composite Pa of the lot. The result is the probability of acceptance of the lot as a function of the fraction defective of the product.
I think that this is to agree with the method that you described.