Design of experiment for 2 continuous factors and 1 discrete numerical factor

[#1]

Hi JMP experts

I struggled to decide which DOE to use for my experiment. I have 2 continuous factors and 1 discrete numerical factor (3 levels). The goal is to optimize the combination of these factors to achieve maximum Y responses (I have 2 Y responses).

What would be the best DOE to use?

I would appreciate your help!

Thanks!

[#2]

You can create this design quite easily in the Custom Design platform. Analysis in Graph Builder or Fit Y by X for lots of visualizations and modeling in the Fit Model platform, standard least squares fitting personality presuming your responses are continuous/numeric in nature...if something else a different fitting personality is required...but that depends on the specific nature of the response data type.

[#3]

Oops, I didn't see @P_Bartell response before I posed this.

You may want to try the Custom Design.  

     DOE=>Custom Design

it works by having you input the specifics of your experiment and then builds the DOE for you.

[#4 · Accepted solution]

Hi @stat_mr_h,

Welcome in the Community !

Before recommending a specific platform or type of design, some questions to help you frame your DoE and topic :

• Factors in the study : In the case described, you listed only 3 factors. Have you already screened and filtered out some factors that could influence your system ? Are there only these important and active 3 factors ?  
• Factors' ranges : How confident are you about the factors' ranges : do you think that the optimal point will be inside your defined experimental space ?
• Response measurement/variability : Have you already some knowledge about the measurements variability in order to evaluate the number of runs needed ? What is the repeatability/reproducibility of your measurement system ?
• Difference in response levels : Linked to the two previous items, are the factors' ranges broad enough so that your experiments have significant different response measurements, taking into account measurement variability ?

About the use of specific design types and platforms, this JMP quizz could be a good starting point to have a first recommendation about which type of design to try first : DOE Quiz (jmp.com)

If you have any doubts about the topics and questions asked before, here is a possible recommandation on how to start :

1. In order to check if your factors' ranges enable to see differences in the responses, and possibly have a first assessment of response variability, I would start with a Screening design (using the platform Custom design, and using a simple design (D-optimal) to check main effects, and including some centre points and replicates to assess measurement variability) or a more parcimonious/economical Scoping design (not included in JMP by default but very easy to create and analyze/visualize).
2. Once you have created your initial design and checked the accordance of your factors' ranges with responses variability and the ability to detect differences in the responses, you can then Augment Designs. Enter your factors and responses, click on "Group new runs into separate block" and click on the Augment option. You can also change the factors ranges at this step if you had too broad ranges or if you want to move to a different experimental area. From there, you'll be able to specify the model you want, so in your case it would be a good option to click on "RSM" to specify a Response Surface Model, including the main effects, 2-factors interactions and quadratic effects.
3. Analyze the results of your design, adequacy of your model, and check if you're able to find an optimal point. If the optimal area is not yet fully analyzed or there might be some non-linear effects that you can't modelize well, you can augment once again your design and choose a Space-Filling augmentation type. This will create points quasi-randomly and homogeneously in your experimental space, and you'll be able to use other types of models, like Machine Learning models if necessary.

If you are already confident about the factors, ranges and responses, you can also directly create your Response Surface design in JMP using the Custom design platform, specifying all main effects, 2-factors interactions and quadratic effects in the model (or simply clicking on "RSM" button in the model panel). I recommend creating several designs with various number of runs, to better understand the tradeoff between necessary experimental budget and design performances, and help you optimize this compromise. You can create several designs and use the Compare Designs platform to compare their performances, or directly generate several designs with various configurations using the Design Explorer platform.

Hope this answer will help you,