Using DOE to optimize a process

[#1]

Dear JMP-Community,

I want to optimize a process. I have 5 factors (X1 –X5), whereof one is a hard-to-change factor (X3) and 10 response variables (Y1-Y10). Responses are measured with a trained sensory panel (8 – 11 assessors). Each assessor can evaluate 3 samples per whole plot (=day). The assessors evaluate the intensities of the defined attributes (=responses) using an unstructured line scale (0 = lowest intensity; 100 = highest intensity).

I created a custom split plot RSM design with 27 treatments. Each assessor is evaluating all 27 treatments (so each treatment is evaluated more than once to gain a more precise result). For fitting the model, I named the treatments as Sample and used it as Random Effect in my model (so there are 27 samples with 8 – 10 data points (evaluation of a sample by different assessor); in total 224 runs).

I fitted my model as follows:

Fit Model(

    Y( :Y1 ),

    Effects( :X1, :X2, :X3, :X4, :X5 ),

    Random Effects( :Whole Plot, :Sample, :Assessor ),

    NoBounds( 1 ),

    Personality( "Standard Least Squares" ),

    Method( "REML" ),

    Emphasis( "Minimal Report" )

);

Since it is my first design ever, I am unsure whether my design and model are correct. Have I set up my model correctly? And is a normal distribution met enough to fit the model as mentioned?

Are there any errors or do you have suggestions for improvement?

I have attached my design and design evaluation (pdf file) and my data (jmp file).

Thanks for your help!

[#2]

Wow. This is quite a complicated example. I can't see anything wrong with how you have modelled the data.

Because your responses are bound by 0 and 100 then, strictly speaking, they should not be modelled with a normal distribution, as you have suggested in your question. The normal distribution assumes values can take any value from negative infinity to positive infinity. In practice, we can usefully model lots of responses that do not really follow a normal distribution - the normal distribution is often a good enough approximation. In your case, given that the responses are mostly distributed well within those bounds, the normal distribution will still be a useful model. However, if you see predictions from your model that are below 0 or above 100, you can workaround this by using a LogitPct transform to your response variable in Fit Model, which is commonly used for responses that are on a % scale, e.g. %yield. But I don't think this will make much difference in your case.

[#3]

Thanks for your supportive reply