Response surface methodology analysis

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... 

The statistical techniques associated with response surface methodology are concerned primarily with two aspects of the experimentation process the construction of experimental designs that yield data to permit the efficient modeling of the response surfaces, and the analysis of the experimental data and derived response surfaces. 

Now if each of the design points in the central composite design is replicated five times, so that the complete design has 75 runs, then at each design point we can calculate the average response and the standard deviation of the response. The analysis techniques associated with response surface methodology can then be applied to fit separate models to... 

Response Surface Methodology (RSM) was used to investigate the effects of temperature, pH and relative concentration on the quantity of selected volatiles produced from rhamnose and proline. These quantities were expressed as descriptive mathematical models, computed via regression analysis, in the form of the reaction condition variables. The prevalence and importance of variable interaction terms to the computed models was assessed. Interaction terms were not important for models of compounds such as 2,5-dimethyl-4-hydroxy-3(2H)-furanone which are formed and degraded through simple mechanistic pathways. The explaining power of mathematical models for compounds formed by more complex routes such as 2,3-dihydro-(lH)-pyrrolizines suffered when variable interaction terms were not included. 

Response Surface Methodology (RSM) is a statistical method which uses quantitative data from appropriately designed experiments to determine and simultaneously solve multi-variate equations (3). In this technique regression analysis is performed on the data to provide an equation or mathematical model. Mathematical models are empirically derived equations which best express the changes in measured response to the planned systematic... 

Steven Gilmour is Professor of Statistics in the School of Mathematical Sciences at Queen Mary, University of London. His interests are in the design and analysis of experiments with complex treatment structures, including supersaturated designs, fractional factorial designs, response surface methodology, nonlinear models, and random treatment effects. 

Innovations in statistical tools such as multivariate analysis, artificial intelligence, and response surface methodology have enabled rational development of formulations, and such methods allow formulators to identify critical variables without having to test each combination. 

Stone et al. (S29) developed by a mathematical analysis the functional relationship between the rate of extraction of silica from pure quartz in sodium hydroxide solution and time, temperature, sodium hydroxide concentration, and particle size. With the use of response surface methodology, a comprehensive picture of this dissolution process was obtained from a few well-chosen experiments. The fractional extraction of silica can be expressed by a second-order equation. The effect of quartz particle size and temperature are predicted to be about equal and greater than the influence of sodium hydroxide concentration and reaction time. The reaction rate is controlled by the surface area of the quartz. An increase in sodium hydroxide concentration increases the activation energy for the reactions and is found to be independent of quartz size. 

Enormous progress has been made in the direction of systematic formulation development through the use of such statistical tools as multivariate analysis and response surface methodology, and artificial intelligence. 

Optimization of reaction conditions for enzyme assays has traditionally been carried out by varying a single factor and studying its effect on the reaction rate, then repeating the experiment with a second factor and so on until effects of all the variables have been tested. An optimal combination of variables is selected on the basis of these experiments, and the validity of die chosen conditions is verified. Not only is this approach labor intensive, but it also is not well adapted to situations in which the effects of different variables are interdependent, as is frequently the case in enzyme analysis. This traditional empirical approach to optimization has been replaced by newer techniques of simplex cooptimization and response-surface methodology."... 

Application of factorial design and response surface methodology to the analysis of caseins by CE using a... 

Application of Factorial Design and Response Surface Methodology to the Analysis of Caseins by CE using a Neutral Capillary... 

M.I. Acedo-Valenzuela, T. Galeano-Diaz, N. Mora-Diez, A. Silva-Rodriguez, Response surface methodology for the optimisation of flow-injection analysis with in situ solvent extraction and fluorimetric assay of tricyclic antidepressants, Talanta 66 (2005) 952. 

Perez, M.M. and Montero, P. 2000. Response surface methodology multivariate analysis of properties of high pressure induced fish mince gel. European Food Research and Technology 211 79-85. 

J. T. Currie, Jr., A Response Surface Methodology Approach to Optimization in Flow Injection Analysis. Diss. Abstr. Int. B, 46 (1985) 498. 

Optimization. The influence of the reaction parameters on the yield of the reaction were studied using response surface methodology (RSM). A central composite design was used and both canonical analysis of the second-order equation and discussion of the isoresponse curves were used for the interpretation of the results. 

A way to overcome this problem is to generate an approximation of complex analysis code that describes the process accurately, but at a much lower cost. Metamodels offer an approximation in that they provide a model of the model . Clarke et al. (2005) [58] suggested metamodelhng techniques, namely response surface methodology (RSM), radial basis function (RBF), kriging model and multivariate adaptive regression sphnes (MARS) as potentially useful approaches. Computer deterministic experiments have been addressed by Charles et al. (1996) [59], Simpson et al. (1998) [60], CappeUeri et al. (2002) [61] and Aguire et al. (2(X)7) [62],... 

Riddin TL, Gericke M, Whiteley CG. Analysis of the inter- and extracellular formation of platinum nanoparticles by Fusarium oxysporum f. sp. lycopersici using response surface methodology. Nanotechnology 2006 17 3482-9. 

Krishnamoorthy, A., Boopathy, S.R. and Palanikumat, K. (2009) Delamination analysis in drilling of CFRP composites nsing response surface methodology,/ Compos Mater, 43 2885-901. 

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