Can the levels of input factors that arrive at maximum value of response (Maximum is better) considered as optimum in full factorial design ?
In general, the answer is no.
The factor settings used in construction of the DOE experimental setup is not necessarily the optimal factor settings for the experimental system.... the experimental region covered by these points may be far away from the optimal settings, that is why search techniques such as steepest ascent method is coupled with DOE experimentation to successively climb up the response surface, near the region of the optima a planar response surface is not adequate to capture the curvature effects in this region... the lack of fit F test being significant, one switches over to a second order design such as a Box Behnken design or Central composite design to construct a quadratic approximation to the actual response function in the neighborhood of the optimal point, analysis of this fitted quadratic function indicates the nature of the associated critical point: whether it is a maxima Or minima or a saddle point, if the fitted quadratic response function is concave/strictly concave the critical point can be taken as the optimal point ( the approximation to the actual maxima) of the true response surface.
Debopam Ghosh What is response optimizer in regression analysis then in minitab ? When I generate regression model after DOE, it gives an option to optimize based on desirability function.
desirability functions are used in the framework of Multi Objective optimization, they sort of try to attain a compromise among the different objectives ( for examples finding the factor settings that is simultaneously optimal for a set of objective functions, which may be the yield of product A1, A2 and so on)
I suggest you look into the theory and implementation of the desirability functions method, and other multi objective RSM methods, from the book on Response Surface Methodology by Myers, Montogomery and Cook, in this book there is a complete chapter dedicated to multi objective optimization methods and use and implementation of desirability functions approach in Minitab software.
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