Determing n small lot size c=0

[jcc0016]

I am currently working on implementing a sampling plan in my organization as it relates to the sampling of raw materials (bulk chemicals), but am having trouble choosing an appropriate plan. I am leaning towards zero acceptance, as a manufacturer of health care and other direct to consumer products, because if I were to find one defect in the lab we would want to reject the lot.
One lot of chemical can come in multiple containers and some number (n) of these containers will have to be sampled and inspected. I do not see us ever receiving a lot which would come in more than 100 separate containers (actually the max number of containers is probably closer to 50). How would I best determine how many containers should be opened/sampled?
I have been looking at the table created by Nicholas Squeglia, but it stops at a max of 35.
Thank You.

[Stan Hilliard]

I am currently working on implementing a sampling plan in my organization as it relates to the sampling of raw materials (bulk chemicals), but am having trouble choosing an appropriate plan. I am leaning towards zero acceptance, as a manufacturer of health care and other direct to consumer products, because if I were to find one defect in the lab we would want to reject the lot.
One lot of chemical can come in multiple containers and some number (n) of these containers will have to be sampled and inspected. I do not see us ever receiving a lot which would come in more than 100 separate containers (actually the max number of containers is probably closer to 50). How would I best determine how many containers should be opened/sampled?
I have been looking at the table created by Nicholas Squeglia, but it stops at a max of 35.
Thank You.

The most appropriate kind of sampling plans I can recommend will depend on the nature of the quality characteristics. I understand you have bulk chemicals, I presume homogenous powder or liquid, in containers. Can you say more about what you test for? Do you start with numerical measurements to determine if passing, or can you only observe yes/no quality, or both? Or do you count items?

I understand that If you have to reject, it would be the lot and not individual containers. Is the testing nondestructive -- in the sense that the material in a tested container can be used if the lot passes. Are test observations costly enough or time consuming enough that it is extra important to minimize their number? (without losing the ability to detect off-grade chemicals.)

Stan Hilliard

[jcc0016]

In regards to testing, it is not destructive in the sense that when a container is opened it is no loger useable. A container is opened, whether solid or liquid, and a portion or aliquot is removed and tested. Testing would include confirming identitiy and purity, they are not physical measurements. The material is homogeneous. The testing itself is not overly costly, but the cost associated with the analysts time is, escpecially considering the suppliers have been approved through various company procedures and have shown to have an excellent supplier performance over the years. In my industry the accepted sampling plan has been the Sqrt of n (number of containers received per lot) + 1. The methodolgy has been scrutanized as not being "statistiacally valid" so I have been searching for an approach that is.

[Stan Hilliard]

I agree that sqrt of n + 1 is not a very good plan because the exposure to accepting an off-grade lot, as expressed by the oc curves, varies greatly depending on the lot size.

Since you are treating each container as pass/fail, the fact that you are sampling powders and liquids does not make the sampling plan;s decision rule different from any other attribute sampling plan.

I think the governing factor to consider in choosing a acceptance sampling plan is that you are the consumer so you would best use the consumer's point with RQL to evaluate and compare alternative plans rather than the producers point with AQL. This is much easier with plans that are not based on lot size. See my article "An AQL Primer for Purchasing Agents"

The rejectable quality level (RQL) is going to be a larger number than the acceptable quality level (AQL), so RQL doesn't make the description of the plan look as good in a "public relations" sense. But you are also relying heavily on the high quality stemming from your company's supplier practices. The probability of an off-grade lot getting used in your system is not just equal to RQL but to the product RQL*p, where p is the probability that the supplier will send you an off-grade lot -- probably a small fraction. So don't be discouraged by a high RQL alone.

When choosing a sampling plan based on the oc curve there are two approaches -- pick an n, c and determine its oc curve, or pick two points (the producer's and consumer's points) and calculate n and c from that. Since you already know that you will use c=0 it would be best to use the first method.