Response surface methodology limitations

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. 

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. 

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