Variance components analysis - manufacturing process

[#1]

Hi all,

I’m looking to understand the variability associated with a multi-step manufacturing process.  I think the way to do this is to plot the plot using the variability /attribute gauge chart, then use the variability components analysis.  But, I’m unsure of what variability model (crossed, nested, etc) to use.  With that said, let me give some more detail.

Our raw material input (let’s call them cards) goes through two main processes (let’s call them process 1 and process 2).  Process 1 involves placing cards into a machine that chemically treats them.  The machine is not large enough to accommodate an entire lot, so we will treat subsets of the lot sequentially until the entire lot is complete.  These subsets are called sublots and consist of 24 cards. There are two shelves inside the process 1 machine, and each shelf accommodates 12 cards.   We’ve previously found that our results can vary based on which shelf a card ends up on, so we track this as well as the specific position on the shelf.  

Once cards come out of process 1, then move to process 2.  Process 2 chemically treats the cards in a different way and does so in runs of 20.  We typically run cards on process 2 sequentially as they come out of process 1.  So, run 1 of process 2 includes 20 of the 24 cards from process 1 sublot 1.  Run 2 of process 2 includes 4 cards from sublot 1 and 16 cards from sublot 2, etc.

So, if that all makes sense, my question is how to run the variability components analysis for this data set.  For process one, I’m thinking that shelf and position on shelf are nested in sublot.  Then, this is crossed with process 2 run.  But, I’m not sure about this at a conceptual level and really not sure how to make JMP do this analysis.

Any help is appreciated.  Thanks,

-Matt

[#2]

@barnabei , welcome to the community.  I will share some of my thoughts:

1. I agree the shelf is nested in subplot and location on shelf is nested in shelf and these components are nested in lot of raw material and if there is only one measure, measure is confounded with location.

2. I assume you take no measures after the first process step? Only one response variable?  

3. Process step 2 seems independent from process step 2 and there may be interactions between step 1 and step 2 and therefore these could be treated as crossed.

4. Measurements are nested in the study.

5. For analysis, there are a number of things you can do.  I do not believe the built in variance components is flexible enough to handle the complexity of the process you describe. Draw a tree depicting the study. Pay careful attention to the numbers associated with each "layer" of the tree.

6. I would first look at the data graphically (variability plots) and ensure the variability captured is indeed of practical significance.

7. For quantitative, I would likely use analyze fit model adding appropriate crossed and nested terms.

[#3]

Thanks @statman. Some answers:
2. Just one measurement at the end
6. We do typically take time to visualize the data and slice it up an in OFAT manner
7. I'll give that a look. Fit model has always been a bit of a black box to me. If you have a suggestion for some material to get me started learning about this function, I'd appreciate it.

[#4]

How confident are you in the measurement?  Have you ever studied it? Quantified it?

I don't understand why you would look at data in "OFAT" manner?  You will, of course, miss potential interactions.

Analysis should always be Practical>Graphical>Quantitative IMHO.

There are several things you can do to brush up on fit model  JMP offers several on-line options:

https://www.jmp.com/en_us/events/getting-started-with-jmp/overview.html

You can also always use the ? in the software to invoke information about each platform:

https://www.jmp.com/support/help/en/16.0/?os=mac&source=application&utm_source=helpmenu&utm_medium=a...

[#5]

@statman Thanks for sending these over. I'll take a look.

What I mean by OFAT is we can easily look at the impact of sublot, shelf, run one at a time. But, as you mentioned, we'll miss interactions.

[#6]

One other thought to complement @statman 's thoughts is to consider Graph Builder for showing response vs. nesting patterns? You can drag and drop different layers onto the x axis as you see fit interactively to explore mean and variance of the response for the different layers. Mirroring the diagram that @statman suggests you create.