Response-surface designs

O. L. Davies and co-workers. The Design andAna/ysis of Industria/Experiments, 2nd ed., Hafner, New York, 1956 reprinted by Longman, New York, 1987. This book, which is a sequel to the authors basic text Statistica/Methods in Eesearch and Production, is directed at industrial situations and chemical appHcations. Three chapters are devoted to factorial experiments and one chapter to fractional factorial plans. A lengthy chapter (84 pp.) discusses the deterrnination of optimum conditions and response surface designs, which are associated with the name of G. Box, one of the seven co-authors. Theoretical material is presented in chapter appendices. 

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]. 

A complete list of the reaction conditions tested for this response surface design can be found in [76], The center point reaction condition was repeated six times. This was done to measure the variability of the reaction system. Also, the space velocity is kept constant, as it was the least important factor predicted by screening design, for all the reaction conditions. The purpose of this nested response surface design was to develop an empirical model in the form of Eqn (5) to relate the five reaction condition variables and the three catalyst composition variables to the observed catalytic performance. 

Multiple Sensitivity testing Simple regression Response surface designs Multiple regression... 

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... 

Method development and optimization are started with review of the currently available methods within the company or in literature. Available methods are used as a starting point and evaluated against the method requirements set in the method definition. If necessary the method is optimized or redeveloped in order to fulfill the requirements. DOE tools (response surface design) are preferentially applied to obtain the best optimal conditions in terms of robustness. Application of DOE methodology is not new in chromatography and DOE is frequently applied also for enantiomeric separations in Especially in... 

Three- or more-level response surface designs, such as three-level full factorial, central composite (CCD), and Box-Behnken designs, are applied in some case studies. 

To analyze response surface designs, a model is fitted to the data for each response. Usually the results are visualized in response surface plots, showing the change in response as a function of two factors. " These plots allow deciding on the optimal conditions. However, as already mentioned in Section IV, these response surfaces seem not so useful when only small variations around the nominal conditions are examined. 

Finally, a review of robustness testing of CE methods was made and the tests were critically discussed (Section IX). Some researchers use the OVAT procedure, which seems less appropriate for a number of reasons. Some use response surface designs, which also seems less preferable in this context. Another remarkable observation from the case smdies is that only in a minority the quantitative aspect of the method is considered in the responses smdied, even though that was the initial idea of proposing the robustness tests. 

Khuri, A.I., and Cornell, J.A. (1987), Response Surfaces Designs and Analyses, Dekker, New York, NY. 

Myers, R.H., Vining, G.G., Giovannitti-Jensen, A., and Myers, S.L. (1992), Variance Dispersion Properties of Second-Order Response Surface Designs . J. Qual. Technol., 24, pp. 1-11. 

Recall thatm the example above the interest is in developing a predictive model for ecK onent A using spectroscopy. A response surface design is appropriate for the controllable variables because the model is to be used for prediction ani the relationship of some of the variables is considered to be complex. Ta it 2.4 also shows that the pressure and oxygen concentration cannot be comcoUed, but the variation is significant. In this case, a natural design for these 3WO variables also needs to be incorporated into the experimental scheme. M inverse calibration technique can then be used to develop a predictive mofM. 

To summarize, it has been shown that combining the design and environmental variables into a single set for a response surface design not... 

Suppose that a response surface design has been run with n design variables, Xj, x, x, ..., x , and m environmental variables, z, z, z, ..., z. During the experiment the environmental variables are controlled at fixed levels and can be regarded as fixed effects. Suppose that the x s and z s are centered and scaled around 0. In this section, several alternative models for the relationship between the design and environmental variables and the response will be considered. 

In Sections 2.2 and 2.3 we considered the application of response surface methodology to the investigation of the robustness of a product or process to environmental variation. The response surface designs discussed in those sections are appropriate if all of the experimental runs can be conducted independently so that the experiment is completely randomized. This section will consider the application of an alternative class of experimental designs, called split-plot designs, to the study of robustness to environmental variation. A characteristic of these designs is that, unlike the response surface designs, there is restricted randomization of the experiment. 

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. 

The choice of an appropriate experimental design depends on the experimental circumstances. Box and Draper [12] (p. 502, 305) list a series of experimental circumstances that should be considered by the investigator when selecting a response surface design. Many of these considerations also apply to split-plot designs, and to experimental design in general. 

G.E.P. Box, Choice of response surface design and alphabetic optimality, Utilitas Mathematica, 21B (1982) 11-55. 

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