Hi @Tina11,
Welcome in the Community !
It appears that in this first stage, you are in a screening approach, to explore which factors are important and if any 2-factors interactions effects should be considered.
The list of the factors could be set as :
- X1: Factor 1A : Categorical : Choice between 3 candidates
- X2: Factor 1B : Continuous : Concentration for factor X1
- X3: Factor 2 : Continuous : Concentration
- X4: Factor 3A : Categorical : Choice between 3 candidates
- X5: Factor 3B : Continuous : Concentration of factor X4
Are the concentration ranges the same for each candidate in each factor ? If no, nesting may be necessary. To build such design you might have to use coded levels for the concentrations, and use nested factors in the modeling : Nested DOE with continous factors?
If yes, I would probably start with a D-Optimal design with a model assuming 2-factors interactions and quadratic effects for continuous factors X2, X3 and X5, in order to avoid "Yes/No situations" for the responses (each continuous factor will have a min level = 0, an intermediate level, and a max level). JMP would recommend by default 36 runs (minimum 30 runs) with this setup :
DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Categorical, {"A", "B", "C"}, "X1", 0 ),
Add Factor( Continuous, 0, 1, "X2", 0 ), Add Factor( Continuous, 0, 1, "X3", 0 ),
Add Factor( Categorical, {"A", "B", "C"}, "X4", 0 ),
Add Factor( Continuous, 0, 1, "X5", 0 ), Set Random Seed( 466420203 ),
Number of Starts( 4670 ), 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( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
Add Term( {1, 1}, {4, 1} ), Add Term( {1, 1}, {5, 1} ),
Add Term( {2, 1}, {3, 1} ), Add Term( {2, 1}, {4, 1} ),
Add Term( {2, 1}, {5, 1} ), Add Term( {3, 1}, {4, 1} ),
Add Term( {3, 1}, {5, 1} ), Add Term( {4, 1}, {5, 1} ), Add Term( {2, 2} ),
Add Term( {3, 2} ), Add Term( {5, 2} ), Set Sample Size( 36 ),
Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);
Depending if this experimental budget is too high or not, here are some other suggestions :
- Are you sure you want to start your investigation already with 3 levels for the categorical factor ? Can you choose the most dissimilar 2 levels first, to better understand the pattern and trends with the response data, before trying other candidates/categorical levels?
Having 2-levels categorical factors may also be beneficial, as you could have access to other type of designs, like the Mixed-Level Screening Designs (which are efficient and may save you some runs), or simply help lowering the runs number in your optimal design.
- You could also set the estimability of 2nd order terms in your model as "If Possible" which can lower the recommended number of runs (from 36 to 18 runs)
DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Categorical, {"A", "B", "C"}, "X1", 0 ),
Add Factor( Continuous, 0, 1, "X2", 0 ), Add Factor( Continuous, 0, 1, "X3", 0 ),
Add Factor( Categorical, {"A", "B", "C"}, "X4", 0 ),
Add Factor( Continuous, 0, 1, "X5", 0 ), Set Random Seed( 799900606 ),
Number of Starts( 11461 ), 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 Potential Term( {1, 1}, {2, 1} ), Add Potential Term( {1, 1}, {3, 1} ),
Add Potential Term( {1, 1}, {4, 1} ), Add Potential Term( {1, 1}, {5, 1} ),
Add Potential Term( {2, 1}, {3, 1} ), Add Potential Term( {2, 1}, {4, 1} ),
Add Potential Term( {2, 1}, {5, 1} ), Add Potential Term( {3, 1}, {4, 1} ),
Add Potential Term( {3, 1}, {5, 1} ), Add Potential Term( {4, 1}, {5, 1} ),
Add Potential Term( {2, 2} ), Add Potential Term( {3, 2} ),
Add Potential Term( {5, 2} ), Set Sample Size( 18 ), Simulate Responses( 0 ),
Save X Matrix( 0 ), Make Design}
);
If you're interested about nested designs, here are some relevant conversations similar to what you intend to do :
Disallowed Combinations not working
Design of Experiment - Optional Mixture Additives
Hope this first answer may help you,
Victor GUILLER
Scientific Expertise Engineer
L'Oréal - Data & Analytics
