Response surface methodologies

Response surface methodology (RSM) is an optimization technique based on factorial designs introduced by G.E.R Box in the 1950s. Since then, RSM has been used with great success for modeling various industrial processes. In this chapter, we use the concepts introduced in the previous chapters to explain the basic principles of RSM. The interested reader can find more comprehensive treatments in Cornell (1990a), Myers and Montgomery (2002) and in the excellent books and scientific papers of G.E.R Box and his co-workers (Box and Wilson, 1951 Box, 1954 Box and Youle, 1955 Box and Draper, 1987). 

Suppose a chemist wished to investigate the effect of two factors, concentration of a reagent and stirring speed, on the yield of a certain reaction. She already knows that the process has been operating with these values fixed at 50% and 100 rpm for some time and that the average yields obtained under these conditions have been close to 68%. Now she 

The best method for process optimization is response surface methodology (RSM). This process will not only determine optimum conditions, but also give the information necessary to design a process. 

Response surface methodology (RSM) is a method of optimization using statistical techniques based upon the special factorial designs of Box and Behenkini and Box and Wilson.I It is a scientific approach to determining optimum conditions which combines special experimental designs with Taylor first and second order equations. The RSM process determines the surface of the Taylor expansion curve which describes the response (yield, impurity level, etc.) The Taylor equation, which is the heart of the RSM method, has the form  

XI = linear term for variable 1 X2 = linear term for variable 2 

XI-X2 = interaction term for variable 1 and variable 2 XI-X3 = interaction term for variable 1 and variable 3 

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For the PS case, a three-variable Box-Behnken response surface methodology (RSM) design using formulation variables has been carried out. For the RF system, an eight-variable fractional-factorial screening study was done first to select significant factors, and this was followed by two RSM s which were similar in design to the one done for PS. The results have led directly to substantial improvements in both materials. 

Enzymatic hydrolysis of waste paper process optimization using response surface methodology... 

R.H. Myers and D.C. Montgomery, Response Surface Methodology, John Wiley Sons, Inc. New York, 2002. 

Gonzalez, M. et al.. Optimizing conditions for the extraction of pigments in cochineals Dactylopius coccus Costa) using response surface methodology, J. Agric. Food Chem., 50, 6968, 2002. 

Ramirez, J., Guttierez, H., and Gschaedler, A., Optimization of astaxanthin production hy Phaffia rhodozyma through factorial design and response surface methodology, J. BiotechnoL, 88, 259, 2001. 

A. Abdullah, A.V.A Resurreccion and L.R. Beuchat, Formulation and evaluation of a peanut milk based whipped topping using response surface methodology. Lebensm. Wiss. Technol., 26 (1993) 162-166. 

R. H. Myers, Response Surface Methodology, Allyn Bacon, Boston, 1971. 

Murugesan K, Dhamija A, Nam IH, Kim YM, Chang YS (2007) Decolonization of reactive black 5 by laccase optimization by response surface methodology. Dyes Pigm 75 176-184... 

In addition to the basic methods such as SIMPLEX, other key methods for value chain management are the response surface methodology (RSM) to find a global optimum in a multi-dimensional simulation result surface (Merkuryeva 2005) or simulated annealing applied in the chemical production to find optima e.g. for reaction temperatures (Faber et al. 2005). 

Response-surface methodology has also been used to gain theoretical insight into a reacting system (B19) and to determine the order of a reaction (P3). 

Response-surface methodology has been used extensively for determining areas of process operation providing maximum profit. For example, the succinct representation of the rate surface of Eq. (114) indicates that increasing values of X3 will increase the rate r. If some response other than reaction rate is considered to be more indicative of process performance (such as cost, yield, or selectivity), the canonical analysis would be performed on this response to indicate areas of improved process performance. This information... 

Borzelleca JF, OHara TM, Gennings C, et al. 1990. Interactions of water contaminants. I. Plasma enzyme activity and response surface methodology following gavage administration of CC14 and CHC13 or TCE singly and in combination in the rat. Fundam Appl Toxicol 14 477-490. 

Carter, W.H., Jr. (1985), Response Surface Methodology and the Design of Clinical Trials for the Evaluation of Cancer Chemotherapy, Cancer Treatment Reports, 69, 1049-1053. 

Jenkins, M.W., Mocella, M.T., Allen, K.D., and Sawin, H.H. (1986), The Modeling of Plasma Etching Processes Using Response Surface Methodology, Solid State Technol, 29, 175-182. 

Solana, R.P., Chinchilli, V.M., Wilson, J.D., Carter, W.H., Jr., and Carchman, R.A. (1987), Evaluation of the Interaction of Three Genotoxic Agents in Eliciting Sister-Chromatid Exchanges using Response Surface Methodology, Fundamental and Applied Tox., 9, 541-549. 

Parra R, Aldred D, Magan N. (2005) Medium optimization for the production of the secondary metabolite squalestatin SI by a Phoma sp. combining orthogonal design and response surface methodology. Enzyme Microb Technol 37 704-711. 

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