DOE_Custom Design_minimum number of runs

[#1]

Hi,

I am designing an experiment using Custom Design in JMP. I need to know where exactly the "minimum number of runs" is coming from. I searched in the documentation and just found an statement that "It is the minimum number of runs needed to perform the experiment with the effects I’ve added to the model". But this is not enough as a justification in my paper. I need to show the process of obtaining this minimum.

I appreciate any help on this.

Thanks!

[#2 · Accepted solution]

The minimum number of runs is driven by the degrees of freedom required to define your model. Lets take an example of 4 factors. If you have 4 main effects to understand you would need a minimum 5 runs to define the 4 main effects (A, B, C, D) and 1 degree of freedom to delineate the y-intercept. If however you wanted to investigate the main effects as well as two-way interactions you would need a minimum of 11 experiments to define your 4 main effects (A, B, C, D) and the 6 two-way interactions (A*B, A*C, A*D, B*C, B*D, C*D) along with the 1 additional run for the y-intercept. Please note however that this is the bare minimum number of runs required and there are no degrees of freedom left to use for the error term thus the "recommended" number of runs includes some additional runs so that the error term can have some understanding.

[#3]

Thank you very much for your useful explanation!

So, I am trying to figure out how it applies to my case, but don't get it exactly; I actually have 3 variables (each 2 levels) and 2 variable (each 3 levels); meaning 2^3*3^2 design. JMP gives me minimum of 8 runs for just having main effects (not any interactions). How this 8 is calculated?

[#4]

I am making the assumption that your factors are categorical and not numeric continuous. The two level terms require 1 degree of freedom whereas the three level terms require two degrees of freedom. Therefore in your case you need (1+1+1+2+2)  degrees of freedom plus the 1 additional degree of freedom for the y-intercept for a total of 8 experiments.

[#5]

Yes, they are categorical.

Thanks for your answer!

I am just wondering how you calculate it if I add two-way interactions as well?

[#6]

The answer is 27

X1, X2, X3 main effects for two level categorical require 1 each

X4 and X5 main effects for three level require 2 each

X1*X2 and X1*X3 and X2*X3 two way interactions between the two level factors require 1 each

X1*X4 and X1*X5 and X2*X4 and X2*X5 and X3*X4 and X3*X5 two way interactions between the two and three level factors require 2 each

X4*X5 two way interactions between the two three level factors require 4

plus 1 for the y-intercept

I just use the simulate responses under the red triangle and look at the resulting report to get this.

[#7]

Thanks!

I didn't know about "simulate response", so helpful! Thanks for mentioning it.