How to configure factors when another factor depends on each other

Question

Hello,

I'm fairly new to this community. I'd really appreciate any help you can provide!

I'm trying to construct a classical screening DOE, but my factors are a bit funny..

My process is a calendaring process, where the gap between two rolls can be adjusted in 2 ways: mechanically or hydraulically.

Mechanically setting it means there is absolutely no give, while hydraulic adjustment has a little give, depending on how much pressure I apply hydraulically. So my factors are:

- categorical (mechanical vs hydraulic)

- pressure (only adjustable in hydraulic control)

I want to evaluate how my response variable changes between 3 conditions:

- 500 um gap set mechanically

- 500 um gap set hydraulically at 10 psi

- 500 um gap set hydraulically at 100 psi

How do I configure my factors to evaluate the difference between these 3 conditions?

Thank you!

statman · Answer

Here are my thoughts:

1. You want to compare hydraulic to mechanical.  Is one easier to manipulate than the other?  Both factors are trying to do the same thing and that is to take an input material and "squeeze" it down to a desired size. Seems you can change pressure for hydraulic and change actual dimension for mechanical to get about the same gap?  So you could have gap nested in type. To do this you would vary the physical dimension of the gap for mechanical (at 2 levels) and pressure (again 2 levels) for each type.  The execution is not so challenging, but when you do the analysis, you'll need to write the correct model. Y=Type+Gap[Type], or

2. Decide which mechanism you want to squeeze the material and experiment on settings across the multiple rollers to achieve the desired output.

3. Does the process consists of a series of rollers where each have some affect on the thickness/density of the film?  If so, how many?  Can you measure before and after each roller or only at the beginning and the end?  I'm not sure I would say the second roller is dependent on the first.  There may be limitations to the levels you can set for subsequent rollers, but I don't consider those dependent from a statistical perspective...sequential perhaps.

4. There are many options, and I don't know enough about the specifics of your situation to provide appropriate advice...For example, You could measure the thickness of the incoming material and treat it as a covariate (for each roller).

merkis · Answer

I believe asking how to construct DOE when your factors are nested counts as dialogue with experts on setting up your experiment. The example I gave was just to give context on the problem I'm facing, not for this community to help me solve. In fact, I left out other portions of my experiment, such as measurement/material variability, to focus on how to implement this specific experimental design.

If you know how to construct DOE with nested factors, I'd love to hear more. Thanks for the reply!

merkis · Answer

Hello!

Thanks for your response!

Factors being nested is exactly what I was referring to!

I have considered noise and variation in other parts of the process, but left out those details in this post to focus on how to construct a DOE when factors are nested.
I've taken measures to minimize those said variability or accounting for them in the experimental design.

My response variable is film thickness and density out of the rollers.

Going back to the question, how would you construct your DOE in jmp when factors are nested? I can think of many ways this can occur, but some examples are:

1. this specific example, where pressure setting only applies for hydraulic and not for mechanical

2. Say you have a process where your product goes through two rollers consecutively. You want to understand how the roller gaps affect your final density/thickness. Your 2nd roller gap is dependent on your 1st roller gap. For example, if your first gap is 200 um, your second gap (nested factor) would fall somewhere below 200 um. But if your first gap is 100, your second gap would fall somewhere below 100 um. (your 2nd gap would never be higher than 1st gap).

I run into these types of experiments where one factor is dependent on another. I would love any tips on configuring my DOE with these considered!

Thank you