Good, useful and characteristic experiments for (optimal) statistical design of experiments There are more phenomena to which experimental design may be applied than there are alternative valid design strategies.  This should be true, though there are many ways to properly design an experiment.
What are the best "problems" that truly demonstrate the value and nuance for the different types of optimal design of experiments?  (A, D, E, C, V, phi, ....)  
Can you provide books, links, articles, references, or at least good empirically driven opinions? 
 A: This is a work in progress, and it is meant to answer my own question.  (Not complete yet)
Common types of Optimal
NIST provides (link) the following definitions for the types of Optimal Design of experiments.
A-Optimality
[A] criterion is A-optimality, which seeks to minimize the trace of the inverse of the information matrix. This criterion results in minimizing the average variance of the parameter estimates based on a pre-specified model.  The fundamental assumption then is that average variance of the prior model describes overall variance of the actual system.
D-Optimality
[Another] criterion is D-optimality, which seeks to maximize |X'X|, the determinant of the information matrix X'X of the design. This criterion results in minimizing the generalized variance of the parameter estimates based on a pre-specified model.  The fundamental assumption then is that the generalized variance of the prior model describes overall variance of the actual system.
G-Optimality
A third criterion is G-optimality, which seeks to minimize the maximum prediction variance, i.e., minimize max. [$d=x'(X'X)^{-1}x$], over a specified set of design points.  Like $H_{\infty}$ control this minimizes the maximum error given the prior model.
V-Optimality
A fourth criterion is V-optimality, which seeks to minimize the average prediction variance over a specified set of design points.
Requirements and ...
NIST says that the requirements include:

*

*An a-priori appropriate analytic model

*A discrete set of samples points as candidates elements of the DOE

Working
Here are "textbook" statistical analyses.  DOE should apply to them, and if there is a healthy connection between "textbook statistics" and "statistical design of experiment" then they should be relevant for the answer of this question.
http://www.itl.nist.gov/div898/handbook/eda/section3/4plot.htm
The NIST case studies include:

*

*Normal random numbers

*Uniform random numbers

*Random walk (running sum of shifted uniform random)

*Josephson junction cryothermometry (discretized uniform random)

*Beam deflections (periodic with noise)

*Fitler transmittance (autocorrelation polluted measurements)

*Standard resistor (linear with additive noise, violates stationarity and autocorrelation)

*Heat flow (well behaved process, stationary, in control)

