Which design is most appropriate

[#1]

Dear all,
I want to perform a DoE in order to optimize the yield of my extraction. I have 7 continuous factors and 1 discrete factor. My idea is to start with a screening design, choose the most important factors, and then continue with the response surface.
I do not know what is the most appropriate way to do the experiment ? which kind of screening design and which kind of response surface are suitable?
I will appreciate any ideas and suggestions
Many thanks
which design is most appropriate

[#2]

I'm going to presume you know very little, have zero to little experience with DOE. If my presumption is correct, then I would pause and run straight to the SAS "Statistics for Industrial Problem Solving" and complete all the modules related to analysis of data and DOE (and the entire course if you are new to JMP as well). There are many, many questions that need to be addressed before selecting and appropriate design and analysis pathway...IMO too many to answer in a forum such as this.

Here is a link to the course: Statistics for Industrial Problem Solving 

[#3]

Thanks a lot, @P_Bartell and @Mark_Bailey for your feedback

It is true that this is my first experience with DoE but I did a lot of reading including the suggested course on the JMP platform. As I said my objective is to optimize the yield of my extraction and I have 7 continuous factors and 1 discrete factor. The feasibility of the experience in the instrument was tested at different levels then the study domain was determined.

The conclusion of my short journey is as you said @Mark_Bailey to use a DSD. DSD can also determine the quadratic effect and I can get some response surface plot and only  21 experiences are needed (including the 4 runs that JMP suggests). 

But I am a little bit lost with the DSD, is it just a screening design and I will need to forward with a response surface design later? Or DSD is enough for screening and optimization? 

Indeed I have no idea if more than half of my factors are inactive or not (which same to be a condition for DSD)

[#4]

A Definitive Screening Design is a very good possibility as your best initial experiment...but not so fast. I'm a little concerned wrt to your lack of confidence in effect sparsity holding within the system. The DSD does rely on this property being present. There are other questions you haven't answered yet. Like are there any restrictions on randomization that might make blocking or a split plot type design appropriate? Are there nuisance factors that might be good candidates for covariates or blocking? My last question is have you investigated a D - optimal design which is more model driven vs. a DSD? D - optimal designs can also be used for screening purposes. Perhaps a main effects only model driven D - Optimal design to identify the active main effects could be a way to go as well? Too many unanswered questions...and nobody can answer the 'Or DSD is enough for screening and optimization?' question. In fact I think an alternative way to address that issue is run your first design...whatever that is...and if the results are sufficient to solve your practical problem...then why proceed with further experimentation? My guess is there are other more pressing problems/issues that could be addressed?

[#5]

@P_Bartell  The principle of effect sparsity asserts that most of the variation in the response is explained by a relatively small number of effects. How to be sure that this is holding?  I am only sure that third-order interactions and some two-way interactions are inactive in my system.

There are no nuance factors 

I agree with what you said, "In fact, I think an alternative way to address that issue is run your first design...whatever that is..." that is why I wanted to hear your thoughts about starting with a DSD. However, I have one restriction on randomization since changing temperature (one of my factors) from Max to Min values takes time. How to deal with this in DSD?

Thanks in advance 

[#6]

Without apriori knowledge of system effects it's impossible to be 'sure' effect sparsity is holding. The only way I know how to 'know' with any degree of certainty is by experimentation itself. You might be 'ok' with a DSD and system devoid of most two factor and higher effects. You still have not answered my question about looking at a D - optimal design focused on main effects. You can get away with a much smaller design than a DSD if your focus is truly screening for main effects. Then spend more of your budget on RSM methods during subsequent experimentation. Last issue is disallowed combinations...the DSD really forces you to run all the prescribed treatment combinations. If there are any combinations that might be dangerous of you know 'won't work' on a first principles basis...then a D - optimal design can accommodate disallowed combinations. Just things to consider.

[#7]

I should read a bit about D-optimal design. Do you have some useful links I can look at?

[#8]

A good place to start looking is the JMP online library of on demand webinars. DOE and optimal design strategies are discussed in numerous webinars.

[#9]

Some of my thoughts though Pete and Mark have provided good suggestions.

Not nuance factors, but NOISE factors (variables you have decided not to control into the future for whatever reason (cost/convenience/technological inability)).  It is impossible not to have noise!  For example: batch-to-batch variation of the chemicals, ambient conditions, measurement errors, operator technique, etc.  It is not recommended (by me) to run optimization designs when you don't understand the noise.  It is an inference space issue. If you optimize under one set of conditions (e.g., material lot) and those conditions change in the future, then your model is no longer useful.  Ever wonder why we are constantly optimizing and never get there?

“It is only by knowledge of the subject matter, possibly aided by further experiments, to cover a wider range of conditions, that one may decide, with a risk of being wrong, whether the environmental conditions of the future will be near enough the same as those of today to permit use of results in hand.” -- W. Edwards Deming

"Block what you can, randomize what you cannot" G.E.P. Box

I'm not going to debate the appropriateness of using DSD or any optimality design here, but I will suggest you recognize you will be iterating.  Keep It Simple and Sequential  (KISS).  My advice is to design multiple experiments, consider: what will be separated, what will be confounded and what will be restricted.  Contrast this with what you think you know and what knowledge do you need to acquire to move on efficiently (potential for knowledge gained vs. resources expended).  Predict all possible outcomes and then pick the one that matches your knowledge/resource comparison.

I prefer Box's RSM which isn't doing one central composite design, but sequential experiments added together to map the surface.

If you are going to impose restrictions, you are in the world of split-plots.

No one knows the right experiment ("The best design you'll design is the design you design after you run it" Ross).  Design selection is situation dependent and quite honestly you have not provided enough information to give that advice.  Also realize that whether the experiment you pick gets you what you want or not, you will learn something (Perhaps, postmortem, we can tell you what it died of).

[#10]

When you are ready (i.e., you feel your background is comfortable), then I recommend using a Definitive Screening Design for your first experiment to improve yield.