Basic Experiment-Mathematical Modeling

General form of mathematical model for a research subject has been defined in Sect. 2.1.1  

Let us stick to response geometrical interpretation of black box with two input factors. A simple graphic system with x-y coordinates is sufficient for this. One may insert values of variation levels of one factor on one axis, and those of the other factor on another axis. Each black box status will have a corresponding point in the surface. As has been said in Sect. 2.1.3, factors are defined by their domains. This means that each factor is defined by its minimal and maximal values where it may be changed continuously or discontinuously. If the factors are concordant then those limits in the plane form a rectangle within which are the points that coincide with black box statuses. Dashed lines in Fig. 2.28 mark the limit values of the domain of factors and full lines the limits of concordant domain of factors. To present graphically the response values, we use the third axis of the coordinate system, so that the response surface has the shape given in Fig. 2.29. 

The area where the response surface has been constructed is called the factor space. The area taken by factor axes is often considered as the factor space. A response function does not have to be geometrically interpreted in a three-dimensional space for a research subject defined by only two factors. For such a presenta- 

Design of Experiments in Chemical Engineering. Zivorad R. Lazic Copyright 2004 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-31142-4 

Point M in the figure is the optimum that by one definition of the research problem objective should be determined. Each intersection line in the plane is a line of constant response values and is called contour lines-contour diagram. 

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Basic Experiment-Mathematical Modeling 327 Table 2.140 Central composite rotatable design 25 1 +2x5 + 6... 

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