# Getting Stuck Choosing a Sampling Plan

A

#### Amonhotep

In a hospital pharmacy in the Netherlands we produce certain drugs in small lots consisting of about 20 units (bottles). For the analysis of the content of the active substance we are exploring possibilities to use statistical methods for the sampling and analysis. The problem is that the analysis is costly and when the sample size is too large we do not have any units left for the patients.

What I read in text books is that we can implement a single sampling plan by attributes, but the problem with it is that those attributes plans only say something about rejecting or accepting the lot and nothing about the quality of the produced drugs. The main reason for the analytical test of the lots is to get insights whether or not the drugs we produce have a good quality (the content has to lay between the limits of 90-110% of the theoretical content) and that we want to monitor this. I also read about sampling by variances, but the problem with this is that the data requires a normal distribution. Data from past records showed no normal distribution, so sampling by variances is not allowed I think.

Do you know any other sampling strategies to use for my particular situation where we can do some statistical quality control with small samples from small lots?

Harmen

btw, I'm not sure this is the right sub-forum, because my question is about both sampling and SPC.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Yes, does sound like SPC would help, with some amount of sampling.

A few questions:

The sampling is destructive. The entire bottle is lost?
Are the 20 bottles filled from one (batch) supply that is made up, or is the making up of liquid (is it liquid or pills?) for the 20 bottles completely independent from bottle to bottle? If the 20 bottles come from one batch, seems like just a sample of the batch would be sufficient, I would think.

A good plan would be once you decide what proportion (if it is less than 100%) of the batches are to be sampled, set up a random number generator (even a dice roll would work) to see if the batch is to be sampled. Then plot the results in the order produced on control charts. If we are dealing with pills, a way to randomly pick a pill or two from the batch could be developed.

A

#### Amonhotep

Thanks for your quick reply, I've also been thinkin of what you suggest, but I encounter a few problems:

We make different types of drugs in this small quantities. Most of the drugs are liquids, but also some capsules and suppositories are among them.

To produce the drugs, we make one batch for example of 2L of a liquid and we fill this out in 20 bottles of 100 mL, or for capsules we make 10 grams of powder and fill it in 20 500mg capsules.
This does not mean all the individual dosage forms contain the same content of active substance because for suppositories and suspensions for example the active substance (which does not dissolve) can sink to the bottom during the filling process. This way the bottles which are filled at the end can contain more active substance than the first bottles.

The sampling is destructive, the sample is partially or completely used for the analysis and opened containers where a certain amount of drug is taken from is not allowed to reach the patient.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Okay. Personally, I would split this into two problems:
- Inconsistencies within the products from the batch due to imperfect blending
- What is the strength of the batch

If you solve the first problem, that helps simplify the sampling.

But, if you aren't going to deal with the blending as a separate issue, I'd go with one bottle out of every 21 liquid bottles (random) and one pill out of every bottle at least as a start. If the SPC shows things are well in control at better than the tolerances, then you could relax the sampling. If there are a lot of problems, I'd try to identify if you are dealing with the overall batch is okay but not homogeneous, versus the overall batch is bad. That would require multiple samples within each batch for a while to see which is the issue. But you would need to switch to some form of troubleshooting / causal analysis routine to fix the problem

If you need a technical basis, there is always Z1.4 / MILSTD 105 sampling plans. True, these are for go-no go, but they would be conservative for measurement sampling.

#### Bev D

##### Heretical Statistician
Super Moderator
I agree that a continuous data SPC chart (I, MR with BOTH control limits and spec limits) would be helpful. the control limits will tell you if anything changes and the spec limits help tell you how capable you are and if there is a change that might signal bad product. (I have used this approach fairly successfully for the type of situation you describe)

I might also suggest using a first piece and last piece sample plan (Not random) for those processes that have non homogenous filling...

A

#### Amonhotep

Thank you both very much for your advice, I think I will apply a continuous data SPC chart with individual X. I will use random sampling for the processes where it is reasonable to assume the product in all containers is homogeneous. For the processes where I can not assume the process is homogeneous I think I will apply a first and last piece sampling plan.

For the most products these methods will work out. The only products the methods are not applicable to are the ones we produce only a few times a year. I think for those products we can not gather enough data points to make a control chart. Do you have suggestions to solve that problem or is the best way to monitor those products on a non-statistical basis.

#### Steve Prevette

##### Deming Disciple
Super Moderator
The only products the methods are not applicable to are the ones we produce only a few times a year. I think for those products we can not gather enough data points to make a control chart. Do you have suggestions to solve that problem or is the best way to monitor those products on a non-statistical basis.
My experience has been it is reasonable to have a control chart with 7 to 12 points on it. Also, keep a running control chart over the years for each product. Even if infrequently made, you can accumulate enough data in the long run to see if things are changing with stops and restarts.

There are proponents of something called "short run SPC" where you estimate the "control limits" from the specifications, but I am not in favor of that method.

Another thing that can be done "across products" is to plot the deltas between the specification and the value measured, even if different products. See "hoteling" in Wikipedia. But this method can be very complex and may end up tripping alarms related to problems with the specifications.

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