Response surface methodology model estimation

In Section 2.2 it was shown that response surface methodology can be applied to enable a researcher to model the effect of multiple quantitative variables on a response with a low-degree polynomial. Frequently, response surface techniques have focused on the mean response as the only response of interest. However, by regarding the variation in the response as an additional response of interest, the researcher can investigate how to achieve a mean response that is on target with minimum variation. In particular, if a researcher replicates each design point in an experiment, then an estimate of the standard deviation at each point can be calculated and used to model the effect of the variables on the variability of the response. 

Response surface methodology (RSM) is a combination of mathematical and statistical tools which is effective for studying and modelling processes where responses are dependent on several operating variables [22]. The model parameters are estimated using the least squares method. In this work a CCD was selected, which is the most used method for fitting second-order models. 

Response surface methodology is designed to allow experimenters to estimate interactions, therefore giving them an idea of the shape of the response surface they are investigating. This approach is often used when simple linear and interaction models are not adequate, e.g., experimentation far from the region of optimum conditions. Here, the experimenter can expect curvature to be more prevalent and will need a mathematical model, which can represent the curvature. The simplest such model has the quadratic... 

The method of response-surface modeling provides a framework for addressing the above problems and provides accurate estimates of the real coefficients, fi. The basic steps of RSM methodology are... 

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