First off, the name is meaningless, as just about all experiments are "designed" as the word is commonly defined, that is, they are "create[d], fashion[ed], execute[d], or construct[ed] according to plan" . There are accidental experiments, but most are designed, so to call this method of experimental design by the name "Designed Experiments" is not helpful in the least. (This is analogous to "Good Laboratory Practices", which every lab worker thinks they are following until they find out that it is a code word from the FDA for a whole slew of regulations.)
But more importantly, the lessons from a designed experiment are incapable of being transferred to another setting. As I've previously said,
"They give you no or little insight as to what underlying principals could be learned and used elsewhere - except to run another DOE. For instance, in a pressure-sensitive adhesive formulation DOE, you may see that adding more tackifier increases the tack. So marketing wants more tack? Then add more tackifier...until you suddenly see a decrease in tack. Now what?
The problem is that the underlying physics drive the results, not an artificial concept like tack. When you see that the tackifier is lowering the plateau modulus (hence more tack) but also increasing the Tg, you realize that you can overdo it. Raise the Tg too much and you have a tack-free material, plateau modulus be damned.
But a DOE will never educate you about this. It will only give directions based on what the inputs were. Garbage in, garbage out. There is a good reason you never see a DOE in Nature, JACS, or pretty much any scientific journal. You don't learn anything fundamental from them. And as soon as we give up our focus on the fundamentals, we are all done."
The overwhelming appeal of designed experiments is that they allow you to change multiple variables with each run and hence the overall number of runs. But engineers long ago learned how to get around that - use dimensionless numbers.
As an example, for fluid flow through a pipe you have to worry about the viscosity, the diameter of the pipe, the density of the fluid and its velocity. That's four variables and quite a bit of work in front of you. But a bright engineer named Reynolds found that if you multiply together the diameter, density and velocity, and then divide by the viscosity, the number is dimensionless. The Reynolds Number was born. The beauty of it is that you only need to worry about your results at various Reynolds numbers, and how have the freedom to change the input variables as you desire and in whatever way is easiest for you. You are in control of the experiments, not the "design" spit out by a computer.
Reynolds had insight into the fundamentals of his system through the Navier-Stokes Equations but such fundamental understanding is not needed. The Buckingham Π-Theorem allows you do derive dimensionless numbers from any of the potential variables for a system. There are dozens of similar dimensionless numbers, but the unfortunate part is that they are mostly used by engineers and seldom used by scientists, and hence, DOE's will continue to haunt us.