How Do you Use Repeated Measurement in Capability Analysis and distribution

[#1]

I need suggestion for the analysis of a data point in multiple measurements. Say, I have potency measurement of a cream drug product from a tube. I have samples from the top, middle, bottom of the tube and hence the measurement for potency. The tube represents the batch and potency is representative of the batch but three measurements are representative of the same batch in reality. In the analysis, should I use the average of the three measurements or use the three data points? Now, for the magic  number of n=30 or more, these three data points from the same tube, should it be considered n=1 or n=3?

[#2]

Let me start by asking a question:

1. What is the goal of the capability analysis study? Is it to quantify the capability of the batch making process? If, yes, read on. If no, then which process are you attempting to evaluate wrt to capability analysis?

Capability Analysis is generally used to determine the center and spread of a distribution of multiple, independent observations of some characteristic in relation to a specification for said characteristic. So generally, in most batch manufacturing processes, one needs to have multiple iterations of the process (that is batches) to establish the capability of the process. So in your case, you've got one single batch, but multiple measurements of the same fundamental process output. So performing capability analysis using the multiple measurements to make a statement about the batch making process in general, is inappropriate.

With respect to the distribution platform, that platform can be used with any characteristic...it might yield some insight wrt to the measurement process so using the platform to simply visualize the population of measurements is entirely appropriate. And just for giggles, since you have observations from three different locations, I'd also use the Fit Y by X platform to visualize the observations by location. Might tell you something about the mean and dispersion of the characteristic within the tube wrt to it's homogeneity within the tube?

[#3]

Before you even get into capability, the type of measurement you are describing, top-middle-bottom, can be a tricky one that you would want to really think about a bit.  Is the assumption that the potency is distributed across the tube following a random distribution that does not worry about position, or do you believe that the position itself has any kind of significance

If the assumption follows the former, then you have to ask yourself why sample 1 tube three times instead of 3 tubes from a similar batch 1 time.    The purpose of rational subgrouping is to maximize the potential for variability due to an assignable cause between the subgroups.   It's important to develop your subgroups to follow that logic.  The normal variation within a single tube is unlikely to represent the full variation between tubes.

If the assumption follows the latter, that there may be stratification within the tube, then you will likely need to use a different type of control chart called a 3-way chart (depending on your version of JMP this may also be called a dispersion chart).  They are also known as between/within charts, and in some place I-MR-R charts.  Because statistics requires 4 names for the same thing.  Anyways.  Don Wheeler (the guy who helped design the MSA tool in JMP..I think) has a good article on 3-way charts here https://www.qualitydigest.com/inside/statistics-column/three-way-chart-030617.html

These are necessary for understanding more complex types of variation where it is understood that the within and between variation are fundamentally different.

[#4]

Thanks Evan.

I am sorry not being clear enough. I have both type of scenarios in fact. For assay or potency, I have 5 stratified samples collected during filling of tubes. This is based on the level of bulk in the storage tank. So I have 5 data points of potency of the same lot. My final assay should be the average of these 5 data points but it is reported as is. Say I have 10 batches of product, which will give me 50 data points. If I don't use subgroup of 5 in this case, I will see N=50 in the report. But using subgroup of 5 will produce a report of N=10. Is this the case? Does it count the variability of subgroup? I will check this but will appreciate your input as well.

For second scenario, in fact this is for content uniformity in a tube (Top, middle, bottom sample analysis from a tube). When I analyze, for example, data from tubes from 10 different batches, I have 30 data points. As said before, without grouping I will get Report of N=30 and with grouping of 3, I will get report with N=10. My goal is to use all data points but get report of actual number of batches. Please advise.

In another scenario, grouping will be difficult. I have three different types: say, 5 and 3 stratifications as well as multiple time points for each batch under stability (o, 3, 6,12,18,24,36 months). How can I accommodate these three different numerical subgroups for single column of response (for example viscosity or assay) during analysis?