Two Common Problems Screening and Optimization

For any synthetic procedure there are a large number of experimental variables which can be varied to define the detailed experimental conditions. It is not likely that all these variables will have a significant influence on the result but some of them will. The first problem is therefore to determine which ones. To this end, it will be necessary to run a screening experiment for sorting out the important experimental variables. This can be accomplished by fitting a low-degree poly- 

The next problem will be to determine how the significant variables should be adjusted to ensure an optimum result. This can be accomplished in different ways  

The method which yields the most accurate predictions of the optimum conditions is to use response surface modelling and to determine a model which also includes square terms to account for curvatures of the response surface. Analysis of the fitted model will then reveal how the experimental conditions should be adjusted to achieve an optimum result. 

Sometimes it is not necessary to determine a response surface model tor locate the optimum conditions. Hill-climbing by direct search methods, e.g. search along the path of steepest ascent [8] or sequential simplex search [9], will lead to a point on the response surface near the optimum. The computations involved in these methods are rather trivial and do not require a computer and will for this reason not be discussed further in this chapter. Readers who require details of these direct search methods should consult Refs. [1,8,9]. 

Which type of design will be most efficient in a given situation is dependent on what type of information is sought. Other aspects will also be involved, e.g. how many individual experiments can we afford to run and how drastic are the approximations we can tolerate in the models. Generally speaking, the number of experiments will increase with the number of variables to study and with the degree of accuracy in the approximation of the response function. 

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