Do not use the one-variable-at-a-time OVAT method

This approach is seducingly simple but it is a poor strategy. It is seemingly successful, but will often lead to totally erroneous conclusions. The method can be used only if the variables are independent of each other. Unfortunately, in most cases the variables are independent only in that sense that they can be adjusted independently. When they exert their influence on the chemical system, the level of one variable may well modify the influence of other variables. This can lead both to compensatory and to amplifying effects. 

Example The influence of variation of pH and the reaction temperature on the yield of a chemical reactions was studied. In a first series of experiments, the reaction temperature was fixed at T = 40 °C, and the pH was varied. A plot of the observed variation in yield vs. pH is shown in Fig. 2.2a. A maximum is observed for pH = 5.0 

In a second series of experiments, the system is buffered to pH = 5.0, and the reaction temperature is varied. The plot of yield variation V5. temperature is shown in Fig. 2.2b. A maximum yield of 70 % is observed at T = 45 °C. By this it is often concluded that the optimum operation conditions would be pH = 5.0, and T = 45 °C. 

This conclusion may be totally wrong if there is an interaction between pH and T. The situation may well be as depicted in Fig. 2.3 where the variations in both variables are given and the function describing the yield variation will be described by a response surface over the plane spanned by the two variables. The topography of the surface is given by the isoresponse contours which show the levels of the yields for different settings of the experimental variables. It is seen that the optimum yield will be 97 %, and that the conditions for this will be at pH = 3.6 and T = 55 °C, which does not at all correspond to the results obtained by the one-variable-at-a-time study. 

By varying one variable at a time, a false maximum was found. The search terminated at a point on a rising ridge of the response surface. If the initial values of the fixed variable had been different, the search would have found another point on the ridge. This is probably the reason for the common belief that experimental procedures have several local optima. The one-variable-at-a-time strategy is therefore often said to be pseudo-convergent, it will hit a false optimum. Ridges of the kind shown in Fig. 2.5 occur when the response surface is curved and when there 

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