Response surface methodology experimental designs

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 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. 

The statistical techniques associated with response surface methodology are concerned primarily with two aspects of the experimentation process the construction of experimental designs that yield data to permit the efficient modeling of the response surfaces, and the analysis of the experimental data and derived response surfaces. 

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. 

In summary, reaction flavors are complex systems and are strongly influenced by changes in reaction conditions. As the number of reaction condition variables increases so does the possibility of variable interactions or synergies. Without appropriate experimental designs it is not possible to assess the contribution of each variable singly and in concert. Response Surface Methodology is another tool for understanding the effects of reaction conditions on Maillard type flavors. 

In several cases, we highlighted theoretical discussions with supporting examples taken from the field of chemistry and process analytical chemistry. In particular, a simple calibration example using UV spectroscopy was selected to provide the reader with a familiar point of reference. In this way, the topics of experimental design and response-surface methodology were presented in a fashion that should help the nonexpert see the benefits of this approach prior to implementation. For the user who is unfamiliar with DOE methods, we hope our approach has provided a useful introduction. 

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 ... 

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. 

CE also suffers from several weaknesses as an analytical technique (e.g., adsorption of charged species to the capillary wall, presence of Joule heating). Hence, it is important to be able to determine optimal conditions in CE method development (23). Various chemometric-based techniques including multivariate experimental design and response surface methodology have been devised to help optimize the performance of a system (23-26). 

Response surface methodology (RSM) is a method of optimization using statistical techniques based upon the special factorial designs of Box and Behenkini and Box and Wilson.I It is a scientific approach to determining optimum conditions which combines special experimental designs with Taylor first and second order equations. The RSM process determines the surface of the Taylor expansion curve which describes the response (yield, impurity level, etc.) The Taylor equation, which is the heart of the RSM method, has the form ... 

If on the other hand we have developed a formulation or process but we wish to predict the response(s) within the experimental domain, then we must use an appropriate design for determining mathematical models for the responses. This and the method used (response surface methodology or RSM) are covered in chapter 5. These 3 subjects are closely related to one another and they form a continuous whole. 

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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