Design of experiment for 2 categorical factors and one continuous factor

[#1]

Hi JMP experts

I struggle in deciding which DOE I should use for my experiment. I have 2 categorical factors ( 3 levels each), one continuous factor and the response is continuous (growth rate). The goal is to optimize the combination of these factors to get maximum growth.

What would be the best DOE to use?

I would appreciate your help!

Thanks!

A

[#2]

Hi @ScientistNMC11,

From what you describe, you seem to already have screened out significant/important factors and want to optimize your response.
So you may be interested in Response Surface (but not very appropriate here since you have only one continuous factor) and I-Optimal designs.

With very few factors (and only one continuous) and a target to optimize one response, the easy way to design your DoE is by trying the "Custom Design". It will give you flexibility about which effects you want to see : main effects, interactions, quadratic effect for the continuous factor, ...
By doing so, you'll be able to have the best number of experiments depending on the level of details you want to have.
For example, if you want to estimate all main effects, interactions and the quadratic effect for the continuous factor, JMP recommends 27 runs (minimum 15 runs).

Depending on your experimental budget, you can add more runs (with replicates or by adding centre runs), or decrease the number of runs (by changing estimability of quadratic effect and/or interaction effects to "If Possible" instead of "Necessary"). You can also change the optimality criterion to I-optimal (red triangle next to Custom Design, Optimality Criterion).

At the end, always try several designs and compare them, to see how the design changes affect the prediction precision/variance, the aliases, the power for effects, ...

I hope it will help you

Victor 

[#3]

Hi Victor

Thank you so much for your reply!

By selecting custom design, I-optimal design and choosing to estimate all main effects, interactions (3rd) and RSM with number of center points 2 and number of replicates runs 3, I got a design of 24 runs and not 27 runs. 

The max of the continuous factor is 0.5 and min is 0.05.

I am planning to use the design to conduct my experiment. Please let me know if I am missing something.

I appreciate your help!

Thanks.

A

[#4]

Without alot more information it's problematic to recommend a specific experimental design. Just a few questions that need answers:

1. Do you have constraints on number of runs?

2. Are there any factor combination constraints?

3. How accurate and precise is the measurement system?

4. Are there any restrictions on randomization?

5. Is blocking or some other randomization constraint technique a good idea?

6. What model structure are you attempting to estimate?

And on and on...I'll let others add to the conversation.

[#5]

Hi Bartell,

Thanks for your feedback!

I don't have constraints on number of runs, any factor combination or randomization. I would like to use the generated design to conduct my experiment. The response is the growth rate of microorganism 2 so it will be calculated from the OD growth curves and the continuous factor is the percentage of microorganism 1 in the suspension. The other two categorical factors consist on the growth phase of each microorganism (3 levels: lag, exponential and stationary phase).

Thanks for your help!

A 

[#6]

7. Are you sure you are including all factors of interest in the experiment. What factors are to be held constant? Should some of the constants be varied and included as well. I have run plenty of designs where the last factor that was brainstormed turned out to be the influential factor.

[#7]

First, welcome to the forum. I think Pete's advice and line of questioning is right on.  

Sorry if I have interpreted your query wrong, but it sounds more like you are trying to "pick a winner" rather than understand causal structure.  You seem to want to use experimental design as a means of creating all off the possible combinations so you can pick the best combination.  This is not how I would use experimental design.  Design selection is best done after sufficient situation diagnostics have indicated what knowledge you have and what knowledge you need to get.  The process is almost always iterative.

There may be some helpful information in this thread:

https://community.jmp.com/t5/Discussions/Simplifying-steps-in-DoE/m-p/479781#M72428

[#8]

Hi Statman

Thanks for your feedback.

I am using this opportunity to learn about DoE as I am at the level of beginner!

Yes I am trying to "pick a winner" to be able to carry out a lab experiment ! I would appreciate very much your recommendations/directions to better understand DoE.

Thanks.

A

[#9]

"...to better understand DOE." I suggest completing the entire SAS "Statistical Thinking for Industrial Problem Solving" online course. Here is a link to the landing page. The course is no cost to you. All you need is a web browser and curiosity. You don't even need JMP...since when you are in the course modules you are running JMP Pro (independent of whatever version of JMP you may have installed on your computer) in a virtual machine environment.

SAS "Statistical Thinking for Industrial Problem Solving" 

Reason I suggest the entire course is there is there is lots of content in the non DOE and modeling modules that will invariably come into play as your expertise in DOE methods matures.