Uniform Shell Designs????

Question

Anybody heard or used these type designs? I've got a customer that seems fond of them. From what I can tell by digging on the web (and there isn't much...so maybe they are flawed in some way or have gone by the wayside with optimal DOE?) they appear to be some sort of specialized space filling type design with some unique rotatable characteristics of the array of treatment combinations within the experimental space? They appear to be close to I optimal designs from a number of runs perspective and adept at fitting RSM type models. Any thoughts, feedback, reactions would be much appreciated mostly just to educate yours truly.

Peter_Bartell · Answer

Tom:

Thanks for your thoughts and information regarding uniform shell designs. I managed to find Doehlert's original paper and skimmed through it. My cursory evaluation is very congruent with yours. Not the type of designs I'd think of off the top of my head...but another arrow in the quiver.

Peter_Hersh · Answer

Hey Tom thanks for the summary.  Peter I ran into the same thing last year and found this reference as well. http://hera.ugr.es/doi/1500448x.pdf where the go over two simple Doehlert designs.

tom_donnelly · Answer

Peter,

To my knowledge Uniform Shell Designs have been around since 1970 when a DuPont statistician, Dave Doehlert, published this paper.

Doehlert, D. H. (1970), "Uniform Shell Designs,' Journal of the Royal Statistical Society, Ser. C, 19, 231-239.

I don't believe Uniform Shell designs are considered space-filling designs.  Although JMP has a "Uniform" Space-Filling design, those points are not "on a shell" but "minimizes the discrepancy between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution."  This Uniform design is compared to Latin Hypercube and Sphere-Packing space-filling designs in the DOE Users Guide.

I couldn't find a reference to Uniform Shell designs or Doehlert in the JMP DOE Guide.  I think of these Doehlert designs as alternative symmetric designs to the Box-Behnken and Central-Composite RSM designs. Like other classic designs, once you have real-world factors and constraints, they may not be viable.

I see that MODDE by Umetrics offers Doehlert designs for 2-20 factors.  Hamada and Wu's textbook on "Experiments - Planning, Analysis, and Parameter Design Optimization" contains a table of Uniform Shell Designs showing there are 7 runs for 2 factors, 13 for 3 factors, 21 for 4 factors and 31 for 5 factors.

Here's one more link to a paper discussing these designs and some other variants. http://www.dtic.mil/dtic/tr/fulltext/u2/a270656.pdf This author, Ron Crosier,  was a former DuPont statistician who knew Doehlert.  I worked with him at the Army.  In short if symmetry is your thing these designs are interesting, but that's not always the real-world.

Hope this gives you food for thought.

Tom