DOE: 2/3/4 projectable designs in Custom Designer?Hi, a customer asked me if it is possible to create "projectable" designs in the Custom Designer.
A projectable design he specified as a design of let's say n factors, where I could e.g. take any 3 of the n (>3) factors and they will build a full factorial design itself. Then it is called a 3-projectory design.
I didn't come across this before, so I thought our DOE champions my can provide some insight 
Thanks
Re: DOE: 2/3/4 projectable designs in Custom Designer?Hi @martindemel ,
We do talk about projections in DOE. For example, you might have heard that the 3-factor projections of a 6-factor DSD are all equivalent and can estimate the full RSM for all 3 factors.
I think that your customer is probably asking about 2-level designs. The fractional factorial 2-level designs have projection properties like this.
Imagine the 2^3-1 fractional factorial - that is, 2 levels, 3 factors, 4 runs. There are 3 2-factor projections (X1/X2, X1/X3, X2/X3). All 2-factor projections are full factorials for those factors.
2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design2^3-1 design
2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design2-factor projections of 2^3-1 design
You can then extend this to higher numbers of factors. All the 3-factor projections of the 2^4-1 fractional factorial are full factorials. And all of the 2-factor projections of the 2^4-2 fractional factorial are full factorials.
There is no direct way to ask for projection properties in Custom Design. But you can create fractional factorials that have the projection properties that you want. Using the classical design tools in JMP is probably the easiest way.
I hope this helps.
Phil
Re: DOE: 2/3/4 projectable designs in Custom Designer?Supersaturated design may also be worth mentioning if the requirement is to experiment in more factors than runs available.
Re: DOE: 2/3/4 projectable designs in Custom Designer?The first two replies strictly answer the question very well. I offer another perspective.
Custom Design uses the coordinate exchange algorithm with an objective function to search for an optimal or nearly optimal design. There is no objective function that I know of for projection, certainly not in JMP, so strictly speaking, Custom Design is incapable of searching for a design with such a property.
Why does projection matter? When the design methods were limited to regular fractional factorial designs, the inherent confounding in low-resolution designs restricted estimation: you could or could not estimate a model parameter. The principle of sparse effects suggested that you were likely to eliminate factors from the model in a screening situation and benefit from projection (less confounding, more estimates were possible). The benefit of projection has more to do with the hand calculations that require balance than anything else. Methods and mindsets have changed over the past century. We do not estimate parameters by hand anymore unless you are a statistics major. The correlation of estimates is undesirable but not fatal when we use regression analysis. The flexibility of Custom Design and regression analysis overwhelms the requirement for projection in practice. I would use the Alias optimality criterion to achieve the best estimability with a design. (A DSD is a special case of an alias-optimal design.)
Re: DOE: 2/3/4 projectable designs in Custom Designer?Thanks a lot, this is really helpful explanation from all of you three!
