I have a question about how to deal with zero content in a mixture DOE when the type of this mixture component is also included as a factor. As an example, I have 3 mixture components, surfactant, solvent, and water, and each of their contents ranges from 0% to 100%. I also have 1 categorical factor, surfactant type, with 2 levels – type A and type B. I included the main effects and the two-way interactions in the model. The DOE I obtained does not account for the scenario where the surfactant type should not have an effect when surfactant content was zero. As shown below, based on the prediction profiler, the predicted response for surfactant A and surfactant B are different when surfactant content is zero, and this is not realistic. What can I do to solve this problem? The JMP file is attached. Thanks for your help!
One solution to avoid constraining the surfactant range to values greater than zero is the following.
First, the nonsense predictions you get are due to two terms in your model: Solvent*Surfactant Type and Water*Surfactant Type.
Replace these two terms by the following three-way interactions: Surfactant*Solvent*Surfactant Type and Surfactant*Water*Surfactant Type (1st pic below).
The two two-way interactions you removed should be ignored from this point on.
The two three-way interactions you included should be used later while modeling the response data.
This way, when Surfactant = 0, these three-way interactions will forcedly be zero too.
Since these two three-way interactions are the only means by which the surfactant type can interact with any other mixture component, the profiler can only predict one value for the response for a given combination of water and solvent levels when Surfactant = 0, i.e. regardless surfactant type (2nd pic below).
Besides, it makes sense to think that interactions of solvent and water with surfactant type should be proportional to the quantity of surfactant.
PICTURE 1
PICTURE 2
