[R] Difficult experimental design questions

[Spencer Graves]

  What is available to help design experiments with non-standard 
requirements?

I have a recurring need to solve these kinds of problems, with deadlines 
of next Wednesday for two sample cases. The first of the two is "mission 
impossible", while the second is merely difficult. The following 
outlines briefly the two problems and the approach I'm currently 
considering. I'd appreciate suggestions either of available software or 
of general approaches. I also have a recurring need to solve this kind 
of problem, so ideas that would take longer to develop could also be 
useful.

MISSION IMPOSSIBLE: 4 factors, 3 levels each, in either 6 or 8 plots 
split in 2 using one of the 4 factors. Because of the split plot 
structure, any model estimated from the 3 between-plot factors will have 
only 6 or 8 distinct combinations available. However, a full quadratic 
model in 3 factors has 10 coefficients. This means that we could only 
estimate models containing subsets of the coefficients. I therefore plan 
to compare alternative designs primarily in terms of their "estimation 
capacity" = percent of models of certain types that are actually 
estimable, following Li and Nachtsheim (2000) “Model Robust Factorial 
Designs”, Technometrics, pp. 345-352. I propose to start with a 
half-fraction of a 12-run Plackett-Burman in 6 runs and a 2^3 in 8 runs, 
then move selected points to a middle value to obtain 3-level designs to 
compare in terms of estimation capacity. After I get the 3-factor 
design, then I can split each of those runs into 2 plots for the 4th 
factor. The problem is complicated because the client already knows that 
at least 2 of the between-plot factors should be highly significant.

MERELY DIFFICULT: 10 factors with 6 at 3 levels and 4 at 2 levels in 
either 12 or 24 plots split in 2 on one of the 3-level factors. This 
problem is easier, because we have more runs and can rely more on effect 
sparsity / tapering of effect sizes, following Burnham and Anderson 
(2002 ) Model Selection and Multi-Model Inference, 2nd ed.; (Springer)

Any ideas, references, etc., would be greatly appreciated.

Thanks,
Spencer Graves