Response Surface Design with 1 impossible configuration

[#1]

Hi,

I've just built an orthogonal response surface design with 8 contiunous parameters with the default axial value : 2.828. The problem is that 1 on my parameters it has no physical sens to go beyond the lower bond. So I have 1 exp that I can't do.

Would you advise me to use a optimal design with a constraint, even if the quality of the plan is less than a response durface design ?

Or just change the impossible value in the plan after it has been created, even if the plan will not be orthogonal after this modification ?

Thanks,

Théo

[#2]

Hmmmm...I'm not sure what you mean by "....even if the quality of the plan is less...". By what measure? Power? Estimable effects? And on and on. But here are my thoughts, I would have started with the optimal approach to begin with for the following reasons:

1. You know you have the constraint...that's one of the primary reasons for using optimal DOE methods.

2. Did you construct a full factorial for the factorial portion (not axial and center points) of the entire design? If so you've created a design that is capable of estimating all possible effect interaction terms up to an 8th order interaction. Do you really need to estimate all these effects? Do you think they are likely to be active? And influential in the system wrt to the responses? The DOE principal of effect sparsity suggests not. Hence using optimal DOE, you specify a model with only the effects of interest you want to detect. Say main, second order interactions, and all quadratic effects. This design would be much smaller from a number of runs point of view...but give you lots of power to detect the effects of interest. So optimal DOE is the efficient path for this scenario.