Optimization task with 2 continuous and 1 discrete (2 levels) factors

Question

Dear Community,

I am dealing with an optimization task and trying to find some references.

Goal of experimentation: Optimization

Input Factors:

* Factor 1: 2-level, continuous
* Factor 2: 2-level, continuous
* Factor 3: 2 level, discrete.continuous

Response:

* chromotography results

Any input is appreciated :)

SDF1 · Accepted Answer

Hi @Aziza ,

I believe you want to use I-optimal criterial for generating your DOE, which I think you will need to use in Custom Design. The other DOE platforms are pre-set with a given optimality criterion, but Custom Design allows you to choose. I believe the I-optimal design is better used when the goal is to find optimum settings.

Hope this helps!,

DS

P_Bartell · Accepted Answer

Can you elaborate wrt to your use of the word 'references'? What are you looking for? If it's just some general guidance, a good place to start would be the SAS "Statistical Thinking for Industrial Problem Solving" online course. Here's a link:

Statistical Thinking for Industrial Problem Solving

Victor_G · Accepted Answer

Hi @Aziza !

Traditionaly in litterature, you can find optimization examples with HPLC or gas chromatography involving classical designs, like Central Composite Designs or Box-Benhken. These designs are often found for different reasons :

* Central Composite Design is often used as the last step of augmenting a factorial design : The study involves generally the screening of different main effects (to know which factors may enable a better resolution for example), and once identified, the design is augmented to include 2 factors interactions and quadratic effects, resulting in a CCD, in order to fully optimize the process and find the best analytical settings.
* Box-Benhken design is used in litterature as one of the design having the best "precision", as more power is available for quadratic power, and this design has uniform precision in the experimental space, often for a lower number of runs than for the CCD. More infos on Box-Benhken : The Open Educator - 4. Box-Behnken Response Surface Methodology

Some links about these designs used in litterature :

* Design of experiments in liquid chromatography (HPLC) analysis of pharmaceuticals: analytics, applications, implications and future prospects (degruyter.com)
* Experimental design in chromatography: A tutorial review - ScienceDirect
* Design of experiments for development and optimization of a liquid chromatography coupled to tandem mass spectrometry bioanalytical assay - Thorsteinsdóttir - 2021 - Journal of Mass Spectrometry - Wiley Online Library

But the "problem" with these classical designs is that they require only continuous factors, which is not your case here.

So as suggested by @SDF1, the best option would be to use the Custom Design platform, enter your responses and factors, your constraints (if any), and then in the model part, click on the "RSM" button : it will automatically add 2 factors-interactions and quadratic effects as well as changing the optimality criterion to I-optimal.

I would highly recommend to generate different "size" designs (with different numbers of total runs and replicate runs number), in order to find the best compromise between the precision you need (variance you can afford in your optimal settings) and your experimental budget.

I hope this first answer will help you have a better idea on how to further proceed,
All the best Aziza,

P_Bartell · Accepted Answer

In addition to my first reply, here is another thought for you. Since you are using chromotography as an analytical step in the determination of results, if you are interested in looking at the spectral data...you'll need to work with some specialized JMP and hopefully you've got JMP Pro, spectral data visualization and modeling techniques. My (I'm retired) former JMP colleague @Bill_Worley  and @Anonymoushave put together a series of articles with lots of methods for visualizing and modeling spectral data. Here's a link to the first article in the series...others can be found by clicking on the links embedded in this first article.Analyzing Spectral Data in JMP/JMP Pro

Bill_Worley · Accepted Answer

Hi @Aziza,

As @P_Bartell  mentioned, we have some options for dealing with the optimization of chemometric data through the Functional Data Explorer.  You can run your DOE and then use Wavelet DOE or Functional DOE to be understand what the optimal HPLC curve is to give you the desired outcome.

Happy to discuss further.

Best regards,

Bill