Response surface methodology empirical models

With the use of such an empirical model, the crushing strength can be optimized with respect to the relative amounts of excipients. The empirical model above can be represented as a surface in the 3-D space, where the axis are x, X2 and CR. Hence, this methodology is called response surface methodology. Good textbooks have appeared in the area of RSM [14,16]. 

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... 

Sukigara, S., Gandhi, M., Ayutsede, J., Micklus, M., and Ko, F. "Regeneration of Bombyx mori silk by electrospinning. Part 2. Process optimization and empirical modeling using response surface methodology". Polymer 45(11), 3701-3708 (2004). 

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. 

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. 

Subsequently, we need to understand how the critical inputs affect the critical outputs (item 4). A second type of designed experiment, called response surface methodology (RSM), is used to accomplish this task. Sometimes we are fortunate and know the equation in advance. For example, the equation for dosage above is D = V x C. However, when the equation is not known, a DOE can be used to empirically fit a model. A response surface study is also presented as part of this case study. 

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