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Construction of thirty-two points specific optimum second order rotatable designs in three dimensions with a practical example

Author: 
Keny Silver J., Tum I.K. and Chirchir E.K.
Subject Area: 
Physical Sciences and Engineering
Abstract: 

This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural levels. The experiment starts from some best guess or “control” combination of the predictor variables (usually coded to x = 0 for this case x1u=30, x2u=25 and x3u =40) and experiment is performed varying them in a region around this center point. We go further to construct a specific optimum second order rotatable design of three factors in thirty-two points. The achievement of this is done with estimation of the free parameters using calculus in an existing second order rotatable design of thirty-two points. Such a design permits a response surface to be fitted easily and provides spherical information contours besides the realizations of optimum combination of ingredients in Agriculture, horticulture and allied sciences which results in economic use of scarce resources in relevant production processes. The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. An example involving Phosphate (x1u), Nitrogen (x2u) and Potassium (x3u) is used to represent the three factors in the coded level and converted into natural levels.

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