Response Surface Methodology mathematical technique

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... 

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. 

The response surface methodology (RSM) is a combination of mathematical and statistical techniques used to evaluate the relationship between a set of eontrollable experimental factors and observed results. This optimization proeess is used in situations where several input variables influence some output variables (responses) of the system. The main goal of RSM is to optimize the response, whieh is influenced by several independent variables, with minimum number of experiments. The central composite design (CCD) is the most common type of seeond-order designs that used in RSM and is appropriate for fitting a quadratic surface [26,27]. 

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for constructing the models and analysing the problems in which several independent variables or controllable factors influence a dependent variable or response (Montgomery, 2003). In RSM, if all the independent variables are assumed to be measurable, then the response surface can be expressed as (Montgomery, 2003) ... 

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