Response surface methodology applications

Carter, W.H., Jr., and Wampler, G.L. (1986), Review of the Application of Response Surface Methodology in the Combination Therapy of Cancer, Cancer Treatment Reports, 70, 133-140. 

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. 

Douglas C. Montgomery is Professor of Engineering andProfessor of Statistics at Arizona State University. His research interests are in response surface methodology, empirical modeling, applications of statistics in engineering, and the physical sciences. 

The approach of using a mathematical model to map responses predictively and then to use these models to optimize is limited to cases in which the relatively simple, normally quadratic model describes the phenomenon in the optimum region with sufficient accuracy. When this is not the case, one possibility is to reduce the size of the domain. Another is to use a more complex model or a non-polynomial model better suited to the phenomenon in question. The D-optimal designs and exchange algorithms are useful here as in all cases of change of experimental zone or mathematical model. In any case, response surface methodology in optimization is only applicable to continuous functions. 

Fassihi R, Fabian J, Sakr AM. Application of response surface methodology to design optimization in formulation of a typical controlled release system. Drugs Made Ger 1996 39(Oct-Dec) 122-126. 

Response Surface Methodology (RSM) is a well-known statistical technique (1-3) used to define the relationships of one or more process output variables (responses) to one or more process input variables (factors) when the mechanism underlying the process is either not well understood or is too complicated to allow an exact predictive model to be formulated from theory. This is a necessity in process validation, where limits must be set on the input variables of a process to assure that the product will meet predetermined specifications and quality characteristics. Response data are collected from the process under designed operating conditions, or specified settings of one or more factors, and an empirical mathematical function (model) is fitted to the data to define the relationships between process inputs and outputs. This empirical model is then used to predict the optimum ranges of the response variables and to determine the set of operating conditions which will attain that optimum. Several examples listed in Table 1 exhibit the applications of RSM to processes, factors, and responses in process validation situations. 

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... 

Stewart, W.H. Application of response surface methodology and factorial designs for drug combination development. Journal of Biopharmaceutical Statistics 1996 6 219-231. 

Myers R.H.. Montgomery D.C. (1995). Response Surface Methodology Process and Product Optimization Using Designed Experiments. New York, Wiley. Droesbeke J.J., Fine J Saporiu G. (1997). Plans d experiencc.s Applications a I en-ireprise. Editions Technip. 

Zhang H, Wu X, Zhang Y, Zhang D (2010) Application of response surface methodology to the treatment of landfill leachate in a three dimensional electrochemical reactor. Waste manage 30 2096-2102... 

Response surface methodology (RSM) is a combination of rrtathematical and statistical techniques used to evalirate the relationship between a set of corrtrollable experimental factors and observed results. This optimization process is used in situations where several input variables influence some output variables of the system. The main goal of RSM is to optimize the response, which is influenced by several independent variables, with minimum number of experiments [9,10]. Therefore, the application of RSM in electrospinning process will be helpful in effort to find and optimize the elec-trospun nanofibers properties. 

Ziabari, M.,Mottaghitalab, V, and Haghi, A. K. in Nanofibers Fabrication, Performance, and Applications, W. N. Chang (Ed.), Nova Science Publishers, USA, pp. 153-182 (2009),. R. H. Myers, D. C. Montgomery, and C. M. Anderson-cook (Eds), Response surface methodology process and product optimization using designed experiments, 3rd ed., John Wiley and Sons, USA (2009). 

Xu, X., liu, Y., Ge, F., Liu, L, and Ouyang, Y. (2013) Application of response surface methodology for optimization of azocarmine B removal by heterogeneous photo-Fenton process using hydroxy-iron aluminum pillared bentonite. Appl Surf. ScL, 280,926 932. 

Juntachote, T., E. Berghofer, F. Bauer, and S. Siebenhandl. 2006. The application of response surface methodology to the production of phenolic extracts of lemon grass, galangal, holy basil and rosemary. Int. J. Food Sci. Technol. 41(2) 121-133. 

Rahiminezhad, M., et al. Application of response surface methodology to synthesize appropriate molecularly imprinted polymer for diazinon. Key Eng. Mater. 605(605), 67-70 (2014)... 

Gong WJ, Zhang YP, Choi S-H, Zhang YJ, Lee KP (2006) Application of response surface methodologies in capillary electrophoresis. Microchim Acta 156 327-335... 

Sim, J.H., et al., 2007. Clostridium aceticum—a potential organism in catalyzing carbon monoxide to acetic acid application of response surface methodology. Enzyme and Microbial Technology 40 (5), 1234—1243. 

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... 

Simplex designs of experiments were first published in 1962 [53], and since then application of this methodology has been constantly growing [31, 54, 10]. Under simplex designing, we understand finding of the optimum of a response function by moving simplex figure on the response surface. Simplex movement is done step by step, whereby in each new step-trial the simplex vertex with the most inconvenient response value is rejected. 

Statistical design of experiment (DOE) is an efficient procedure for finding the optimum molar ratio for copolymers having the best property profile. Based on the concepts of response-surface (RS) methodology, developed by Box and Wilson [11], there are four models or polynominals (Table III) useful in our study. For three components, in general, if there are seven to nine experimental data points, the linear, quadratic and special cubic will be applicable for use in predictions. If there are ten or more data points, the full cubic model will also be applicable. At the start of the effort, one prepares a fair number of copolymers with different AA IA NVP ratios and tests for a property one wishes to optimize, with the data fit to the statistical models. Based on the models, new copolymers, with different ratios, are prepared and tested for the desired property improvement. This type procedure significantly lowers the number of copolymers that needs to be prepared and evaluated, in order to identify the ratio needed to give the best mechanical property. 

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