Screening Design with multiple-level factors and one six-level categrocial factor

[#1]

Dear JMP community. I struggle a bit in finding the right way to perform the DoE especially the screening design!

First i want to find the most important factors with a screening design. Then I want to investigate the important factors in more details with more levels.

I have 4 to 5 multiple factors (between 4-6 levels) and one categorical with 6-levels (the six levels represent different Technologies). For the screening design I use the factors only in 2-levels (low and high) and may add one between for the nonlinearity and the 6-level categorical factor.

Addition infomrations: One simulation run includes always the six-levels from the categorical factor (It takes around 1,5 days for a simulation) this is the consequence of the used model.

What would be the best way for the screening design?

Shall I use a custom design or perform three definitive screening design where i split the categorical factor into three 2-levels categorical factor?

I would appreciate your help!

Thanks

A_Huber

[#2]

One of the hallmarks of screening designs is economy. We sacrifice details in order to ascertain the most important factors (not effects). Why would you have so many levels for a continuous factor? How many runs is acceptable for this case?

Another hallmark of screening is a large number of factors. Four or five is not a large number. You might be able to design an experiment and skip screening in this case. The extra step in a sequence might not be offset later. You can augment any design in JMP for more detailed information (e.g., higher order model terms).

The simulation aspect seemed to come out of nowhere. Is this design for a study of a computer simulation? Then you might want to explore space-filling design. I assume that the simulation contains no stochastic element.

I would not recommend splitting the study up into multiple, parallel designs. You will lost the ability to model factor interactions.

[#3]

Every level I have for the factors represents a component that could be used/ installed in the model. E.g. one factor would be storage capacity with the levels: 215,300,500,630,1000 Liters or battery capacity in different sizes of kWh.

The Number of runs is hard to define - around 50-60 runs by using simultaneously simulation. If more are necessary, I could do that too.

The design will be a computer simulation and it contains no stochastic elements.

[#4]

It sounds like you have made up your mind to use a full factorial design. JMP > DOE > Classical > Full Factorial. Then enter all the factors with all their given levels. The full factorial model is possible with such a design. You do not need any replicate runs.

[#5]

Thanks for the answere.

A full factorial design do not fit the requirmemnts for the number of possible simulations runs.

If i use the full factorial design, it will be 1920 runs.

one 5-level factor

three 4-level factor

one 6-level categorical factor

 --> 5*4*4*4*6=1920  runs

In my opinion it does not sound like a full factorial design, or did I make a mistake?

[#6]

You did not make a mistake. I did. Back at the beginning.

You are confusing 'testing' and 'experimenting.' You are thinking of a test and combinations. Set up a proposed condition, run it, observe the result. Try other conditions and see what happens. Design is about a model. You set up multiple conditions that, in concert, best support fitting the model, then use the model to determine the important effects or to estimate the response for any level you want. The goal is interpolation, especially in computer experiments that cost too much run time for practical applications. Is there any reason that you must include those pre-determined levels? The model does not require such.

If you must use those levels, then I suggest designing the full factorial experiment and making the table. Then select Custom Design and enter the factors from the full factorial as Covariate factors. You will have to specify a model. Then set the number of runs to whatever number is practical for you. Custom design will proceed to find the optimal subset of the full factorial design to meet your number of runs.

[#7]

My first thought is to give appropriate advice, more information regarding your situation may be needed.  What are the response variables?  What are the factors?  How far do you need to move the response variables? etc.

To reiterate Mark's points, a screening design is meant to give a relative comparison of the factors of interest in the selected design space (which includes level setting and noise).  Often the initial screening design will help to prioritize which factors have the largest effect on the response variable(s) of interest and which direction you want to move the design space. The objective being to efficiently move towards the optimum region. Usually, you are not concerned with non-linearity as this occurs within the design space and you are likely to move the space.  More than 2-levels is very inefficient.  Why create a complex model at the base of the mountain? (an analogy is creating a detailed map of Philadelphia when you are trying to get to Boulder, CO.).

What wasn't clear in your first post was this would be run via simulation.  Realize in simulation, an algorithm has already been created in your simulation program.  You may not know what it is (especially if you bought the simulation from a supplier), but it is already there.  Now comes the difficult part....if the algorithm does not contain factors that you want to investigate, the analysis will say those factors have no effect.  There are other opinions, my thoughts are simulation has limited utility for screening. In screening, you are investigating many variables that you don't know have an effect, while simultaneously comparing those factor effects to NOISE. How is NOISE simulated? IMHO, this cannot be realistically simulated.

Admittedly there are some programs that take a long time to run (e.g., FEA) and therefore to conserve computer runtime fractional factorials may be run, but if computer time is no big deal, run full factorials.

[#8]

Thank for does answers!

@statman The responses e.g. to maximize self-consumption,..... Factors e.g. Technology or Storage size

Recoording to the advices, i am probaply going to perform a full factorial design first.

Does make sense to perform afterwards with e.g. the two most important factors a second design with mulitple levels? 

[#9]

Trying to interpret your question so I apologize if I misunderstand...Typically you use screening designs (e.g., fractional factorials) to compare lots of factors in the intended design space.  After determining which of these factors are significant (both practical significance and perhaps statistical significance) you would likely continue to investigate that subset of factors to find optimum regions.  This methodology is what GEP Box calls Response Surface Methodology (not one experiment with factors at >2 levels).  It is the use of iteration of experiments to understand the rather complex surface.  How many experiments it takes is dependent on your current state of knowledge.  And, of course, as new materials and processing technology evolves, so does the response surface...thus continuous improvement.

[#10]

Thank you. It has been a great help to me!