DOE with Three 2 level factors and One 3 level factor that needs blocking

[#1]

Hello,

I am trying to to design a DOE with the following factors:

X1   -1   +1

X2   -1   +1

X3   -1   +1

X4   L1   L2   L3

Due to experimental logistics, X4 cannot be changed easily; it requires an entire day to change. The other factors can be changed easily during each experiment. I was thinking of just doing a full factorial DOE design with X1, X2, and X3; and then repeating that same design for each level of X4. However, this seems overly simplistic and I think it is not the correct way. I am at a lost.

How can I proceed in the DOE design and have a more elegant way to capture this? I do prefer that within each level of X4, all combinations of X1, X2, X3 are included, as those variable are easy to change and it doesn't eat up time/resources. Thank you.

[#2]

You can easily design this experiment with JMP. Select DOE > Custom Design. Define your factors just as they are. Click Easy in the Changes column for X4 and select Hard. You are welcome to pursue all combinations, but this goal is often unnecessary. JMP will determine the best combinations for a given budget (number of runs) and other aspects, such as the terms in the model that must be estimated. I would not think in terms of combinations ("pick the winner") but in terms of the model ("estimability").

What is your background in DOE? Have you read the JMP documentation for DOE? Have you read other books or articles? We like to match the level of our answers with your level of experience.

[#3]

Thank you for your answer. I have taken a couple of courses from JMP, but it has been a few years since then. I understand all combinations is not necessary; but for this particular experiment; it doesn't take much more than pressing a button to change a setting on the equipment. 

[#4]

Please run this script to begin where I left off. I assumed you want to predict the response well throughout the experimental region defined by all four factors.

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Continuous, -1, 1, "X1", 0 ),
	Add Factor( Continuous, -1, 1, "X2", 0 ),
	Add Factor( Continuous, -1, 1, "X3", 0 ),
	Add Factor( Categorical, {"L1", "L2", "L3"}, "X4", 1 ),
	Set Random Seed( 43146839 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
	Add Term( {1, 1}, {4, 1} ), Add Term( {2, 1}, {3, 1} ),
	Add Term( {2, 1}, {4, 1} ), Add Term( {3, 1}, {4, 1} ), Add Term( {1, 2} ),
	Add Term( {2, 2} ), Add Term( {3, 2} ), Set N Whole Plots( 5 ),
	Set Sample Size( 25 ), Simulate Responses( 0 ), Save X Matrix( 0 )}
);