Experimental design response surface

In this chapter the use of statistical experimental designs in designing products and processes to be robust to environmental conditions has been considered. The focus has been on two classes of experimental design, response surface designs and split-plot designs. 

DEMING, S. N. Experimental designs response surfaces, in Chemometrics, mathematics and statistics in chemistry. KOWALSKI, B. R. (ed.), Dordrecht, Reidel, 1981. 

The usual framework of industrial experimentation is response surface methodology. First introduced by Box and Wilson (1951), this methodology is an approach to the deployment of designed experiments that supports the industrial experimenter s typical objective cf systems optimization. Myers and Montgomery (2002) described response surface methodology in terms of three distinct steps ... 

To develop an empirical model for a response surface, it is necessary to collect the right data using an appropriate experimental design. Two popular experimental designs are considered in the following sections. 

The following set of experiments provides practical examples of the optimization of experimental conditions. Examples include simplex optimization, factorial designs used to develop empirical models of response surfaces, and the fitting of experimental data to theoretical models of the response surface. 

Note These equations are from Doming, S. N. Morgan, S. L. Experimental Design A Chemometric Approach. Elsevier Amsterdam, 1987, and pseudo-three-dimensional plots of the response surfaces can be found in their figures 11.4, 11.5, and 11.14. The response surface for problem (a) also is shown in Color Plate 13. 

A Box-Behnken design was employed to investigate statistically the main and interactive effects of four process variables (reaction time, enzyme to substrate ratio, surfactant addition, and substrate pretreatment) on enzymatic conversion of waste office paper to sugars. A response surface model relating sugar yield to the four variables was developed on the basis of the experimental results. The model could be successfully used to identify the most efficient combination of the four variables for maximizing the extent of sugar production. 

Using experimental design such as Surface Response Method optimises the product formulation. This method is more satisfactory and effective than other methods such as classical one-at-a-time or mathematical methods because it can study many variables simultaneously with a low number of observations, saving time and costs [6]. Hence in this research, statistical experimental design or mixture design is used in this work in order to optimise the MUF resin formulation. 

For this last stage, the one-at-a-time procedure may be a very poor choice. At Union Carbide, use of the one-at-a-time method increased the yield in one plant from 80 to 83% in 3 years. When one of the techniques, to be discussed later, was used in just 15 runs the yield was increased to 94%. To see why this might happen, consider a plug flow reactor where the only variables that can be manipulated are temperature and pressure. A possible response surface for this reactor is given in Figure 14-1. The response is the yield, which is also the objective function. It is plotted as a function of the two independent variables, temperature and pressure. The designer does not know the response surface. Often all he knows is the yield at point A. He wants to determine the optimum yield. The only way he usually has to obtain more information is to pick some combinations of temperature and pressure and then have a laboratory or pilot plant experimentally determine the yields at those conditions. 

This model is capable of estimating both linear and non-linear effects observed experimentally. Hence, it can also be used for optimization of the desired response with respect to the variables of the system. Two popular response surface designs are central composite designs and Box-Behnken designs. Box-Behnken designs were not employed in the experimental research described here and will therefore not be discussed further, but more information on Box-Behnken designs can be obtained from reference [15]. 

Figures 5 and 6 show the response surfaces plotted for Property A and Property B, respectively. Note that two variables are plotted at once, with the values of the other variables fixed at levels chosen by the experimenter. The contours in the graph represent constant levels of the response. Fortunately, the computer allows rapid replotting for various levels of the fixed variables, as well as changing the identities of the fixed and floating variables, so that the entire design space can be investigated.

When from initial experiments, conditions that indicate the enantioselectivity of the system towards a given enantiomer pair or towards a limited series of substances are known, one might optimize their separation. To obtain optimal conditions, the different chemometric techniques used for method optimization in classic chromatographic or electrophoretic separations can also be applied for the chiral ones. Different experimental design approaches, using both screening and response surface designs can be In Reference 331, for... 

In reference 20, a typical robustness test is not performed, but a study on the influence of peak measurement parameters is reported on the outcome. The study is special in the sense that no physicochemical parameter in the experimental runs is changed, but only data measurement and treatment-related parameters. These parameters can largely affect the reported results, as shown earlier, and in that sense they do influence the robusmess of the method. The different parameters (see above) were first screened in a two-level D-optimal design (9 factors in 10 experiments). The most important were then examined in a face-centered CCD, and conclusions were drawn from the response surfaces plots. 

---