Response surface methodology experiment design

The strategy for robust design experiments that will be considered in Section 2.3 is based on the statistical techniques associated with response surface methodology. This section will give an overview of response surface methodology, presenting some of the more common experimental designs that have been developed in this area. 

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. 

An alternative approach is to regard the enviroiunental variables as standard experimental variables and to apply the techniques associated with response surface methodology to the combined set of design and environmental variables (see Welch, Yu, Kang, and Sacks [36], Shoemaker, Tsui, and Wu [37], and Box and Jones [38]). This approach can result in considerably smaller and therefore cheaper experiments. 

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. 

Myers, R. H., Montgomery, D. C. (1995). Response Surface Methodology Process and Product Optimization Using Designed Experiments. Wiley, New York. 

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... 

The usual framework of industrial experimentation is response surface methodology. First introduced by Box and Wilson (1951), this methodology is an approach to the deployment of designed experiments that supports the industrial experimenter s typical objective cf systems optimization. Myers and Montgomery (2002) described response surface methodology in terms of three distinct steps ... 

Steven Gilmour is Professor of Statistics in the School of Mathematical Sciences at Queen Mary, University of London. His interests are in the design and analysis of experiments with complex treatment structures, including supersaturated designs, fractional factorial designs, response surface methodology, nonlinear models, and random treatment effects. 

Myers, R.H. Montgomery, D.C. Response surface methodology process and product optimization using designed experiments. Wiley Series in Probability and Statistics, Wiley Interscience, 1995 248 pp. 

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. 

RSM yields the maximum amount of information from the minimum amount of work. For example, in the one-variable-at-a-time approach, shown in Fig, 1, ten experiments were run only to find the suboptimum conditions. However, using RSM and thirteen properly designed experiments not only would the true optimum have been found, but also the information necessary to design the process would have been made available. Secondly, since all of the experiments can be run simultaneously, the results could be obtained quickly. This is the power of response surface methodology. 

Chao Yuan [25] has optimized the preparation process of HP-)3-CDs. Reaction time (A) reaction temperature (B), dialysis time (C) were employed in the single factor experiment. Then, a central composite design of response surface methodology was used with the DS and yield response values. 

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]. 

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