Multi-process DoE

Question

Hello,

I am hoping to get some advice on designing an experiment. I have a process that has 4 steps sequentially. Step A comes first, then step B, then C and finally D. Response is measured at the completion of step 4. Each step has two factors, each with two levels.

I need to model the response as a function of all the 8 factors, taking into account all two-way interactions. I like to make sure no 3-way interaction is confounded with main effects. I have only 60 experimental units (I may be able to change this by little but not much).

I know this falls under the topic of "Multi-step process DOE", but I am not sure how to do this in JMP (or any other software!). I was hoping you could help me with this.

Thank you!

Mark_Bailey · Answer

You are correct. The spread of factors across multiple steps in the process necessitates more than one experimental unit of randomization. Assuming that you have no hard to change factors otherwise, you treat factors in previous steps as further restrictions. So the factors in the last step are easy to change, the factors in the next to last step are hard to change, the factors in the previous step are very hard to change, and so on. JMP is currently unable to design experiments with more than three levels of randomization at this time.

MarkovVaribles1 · Answer

Hello,

Response is continuous and should not be more than 200. Ideally we want it to be in the range 180-200. Going over 200 is failure, but going below 180 is not a failure but poor quality. All factors are continuous at two levels each: low value and high value.

Not sure what you mean by how the noise is handled. A single tool is available for the experiment and used for each step.

I actually tried the custom design and since I have two factors for each step, I used "Hard to change" for the first three steps and "easy to change" for the final step. JMP creates a design with 23 whole plots. The script is as follows:

DOE(
Custom Design,
{Add Response( Match Target, "CD", 80, 100, 1 ),
Add Response( Minimize, "Delta", 0, 10, 1 ),
Add Factor( Continuous, -1, 1, "X1", 1 ),
Add Factor( Continuous, -1, 1, "X2", 1 ),
Add Factor( Continuous, -1, 1, "X3", 1 ),
Add Factor( Continuous, -1, 1, "X4", 1 ),
Add Factor( Continuous, -1, 1, "X5", 1 ),
Add Factor( Continuous, -1, 1, "X6", 1 ),
Add Factor( Continuous, -1, 1, "X7", 0 ),
Add Factor( Continuous, -1, 1, "X8", 0 ), Set Random Seed( 90328190 ),
Number of Starts( 18 ), Add Term( {1, 0} ), Add Term( {1, 1} ),
Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),
Add Term( {6, 1} ), Add Term( {7, 1} ), Add Term( {8, 1} ),
Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
Add Term( {1, 1}, {4, 1} ), Add Term( {1, 1}, {5, 1} ),
Add Term( {1, 1}, {6, 1} ), Add Term( {1, 1}, {7, 1} ),
Add Term( {1, 1}, {8, 1} ), Add Term( {2, 1}, {3, 1} ),
Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),
Add Term( {2, 1}, {6, 1} ), Add Term( {2, 1}, {7, 1} ),
Add Term( {2, 1}, {8, 1} ), Add Term( {3, 1}, {4, 1} ),
Add Term( {3, 1}, {5, 1} ), Add Term( {3, 1}, {6, 1} ),
Add Term( {3, 1}, {7, 1} ), Add Term( {3, 1}, {8, 1} ),
Add Term( {4, 1}, {5, 1} ), Add Term( {4, 1}, {6, 1} ),
Add Term( {4, 1}, {7, 1} ), Add Term( {4, 1}, {8, 1} ),
Add Term( {5, 1}, {6, 1} ), Add Term( {5, 1}, {7, 1} ),
Add Term( {5, 1}, {8, 1} ), Add Term( {6, 1}, {7, 1} ),
Add Term( {6, 1}, {8, 1} ), Add Term( {7, 1}, {8, 1} ), Set N Whole Plots( 23 ),
Set Sample Size( 69 ), Optimality Criterion( Name( "Make D-Optimal Design" ) ),
Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design,
Set Run Order( Keep the Same ), Make Table}
);

Thanks

statman · Answer

Sorry, there is not enough information provided to give sound advice.  What are the response variables?  What are the factors?  Are the factors continuous or categorical? What noise is associated with the process?  How will you handle noise in the experiment? What hypothesized mechanisms are at work? Why do you need Res V or greater?  Can you iterate (Start with screening and then decide whether to move or augment the design space)?  Often with sequential process step designs, you can take advantage of split-plots, but I would need to know more about the process.