Response surface concept, application

One important use of experimental designs is to achieve optimum operating conditions of industrial processes. For a discussion of this application, see Box and Wilson (1951). This paper is extraordinarily rich in response surface concepts. What is the steepest ascent technique discussed in this paper What models are assumed, and what experimental designs are used ... 

It first introduces the reader to the fundamentals of experimental design. Systems theory, response surface concepts, and basic statistics serve as a basis for the further development of matrix least squares and hypothesis testing. The effects of different experimental designs and different models on the variance-covariance matrix and on the analysis of variance (ANOVA) are extensively discussed. Applications and advanced topics such as confidence bands, rotatability, and confounding complete the text. Numerous worked examples are presented. 

For mortality, the individual tolerance concept (using a fixed CBR, or the more elaborate DAM) has been applied to mixtures at the 50% effect level, but more work needs to be done to validate its applicability, and to test it against the stochastic approach. For the stochastic approach, several mixture toxicity studies have been performed where the full dose-response surface could be explained, which is promising. 

Statistical design of experiment (DOE) is an efficient procedure for finding the optimum molar ratio for copolymers having the best property profile. Based on the concepts of response-surface (RS) methodology, developed by Box and Wilson [11], there are four models or polynominals (Table III) useful in our study. For three components, in general, if there are seven to nine experimental data points, the linear, quadratic and special cubic will be applicable for use in predictions. If there are ten or more data points, the full cubic model will also be applicable. At the start of the effort, one prepares a fair number of copolymers with different AA IA NVP ratios and tests for a property one wishes to optimize, with the data fit to the statistical models. Based on the models, new copolymers, with different ratios, are prepared and tested for the desired property improvement. This type procedure significantly lowers the number of copolymers that needs to be prepared and evaluated, in order to identify the ratio needed to give the best mechanical property. 

In addition to the proactive uses of the SRK model described in the two previous sections, it can also be employed retrospectively as a means of identifying the underlying causes of incidents attributed to human error. This is a particularly useful application, since causal analyses can be used to identify recurrent vmderlying problems which may be responsible for errors which at a surface level are very different. It has already been indicated in Section 2.4.1 that the same observable error can arise from a variety of alternative causes. In this section it will be shown how several of the concepts discussed up to this point can be combined to provide a powerful analytical framework that can be used to identify the root causes of incidents. 

Also very broad and of great importance in physics and chemistry is the topic of response theory, where electric and magnetic fields interact with matter. The study of chemical reactions and collisions is the cornerstone of chemistry, where traditional concepts like potential-energy surfaces or transition complexes appear to become insufficient, and the new field of computational chemistry finds its main applications. Condensed matter is a field in which progressive studies are performed, from few-atom clusters to crystals, surfaces and materials. 

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