I created models using Box-Bhenken, Central composite and Optimal designs. After using the random uniform function to allot random responses within a range, I fitted the models.
Can you evaluate these designs using random responses?If yes, how?
I would also like to know how does JMP calculate the number of experimental trials for a givenm model?Are there different formulae for calculation of trials? If yes, where can I look up these formulae?Please provide a reference.
JMP has built in functionality that allows you build a designed experiment and then interactively build a model. There is also built in diagnostics in the design platforms.
When building your design go to the red hot spot at the top left and select Simulate Responses. These will be different for every design you build. When you select this option JMP will automatically put a Model option in your output table.
By selecting the Model hot spot and choosing Run Script JMP will set up Standard Least Squares model and unless you want to change the factors in the model set up you select Run. From there you will get a model output.
I would also recommend that you look at Design Evaluation for each of your designs and you can do that before you select Make Table.
Two evaluations that I think are particularly useful are Power Analysis and Color Map on Correlations. You can learn more about these in JMP Help.
The number of runs is dependent on the number of factors and the whether or not you want to look for interactions. The response surface designs you mention are also meant to determine if you have non-linearity or curvature in your data. They do this by adding center points to the design, both in the middle and on the faces of the hypercube/space. If you are only looking for main effects and you have continuous factors with two levels then the equation to determine the number of runs is 2^n where n is the number of factors. As you start adding interactions the number of runs goes up. Optimal designs are meant to help you limit the number of runs even when you are interested in determining interactions.
A good reference is Box, Hunter, Hunter - "Statistics for Experimenters"