Searching Algorithms for Response Surfaces

When measuring the response is subject to relatively large random errors, or noise, a spuriously high response may produce a false optimum from which the 

Onc-Factor-at-a-Timc Optimization One approach to optimizing the quantitative method for vanadium described earlier is to select initial concentrations for ITiOz and 1T2S04 and measure the absorbance. We then increase or decrease the concentration of one reagent in steps, while the second reagent s concentration remains constant, until the absorbance decreases in value. The concentration of the second reagent is then adjusted until a decrease in absorbance is again observed. This process can be stopped after one cycle or repeated until the absorbance reaches a maximum value or exceeds an acceptable threshold value. 

A one-factor-at-a-time optimization is consistent with a commonly held belief that to determine the influence of one factor it is necessary to hold constant all other factors. This is an effective, although not necessarily an efficient, experimental design when the factors are independent. Two factors are considered independent when changing the level of one factor does not influence the effect of changing the other factor s level. Table 14.1 provides an example of two independent factors. When factor B is held at level Bi, changing factor A from level Ai to level A2 increases the response from 40 to 80 thus, the change in response, AR, is 

In the same manner, when factor B is at level B2, we find that 

Two views of a two-factor response surface for which the factors are independent. The optimum response in (b) is indicated by the at (2, 8). Contour lines are shown for intervals of 0.5 response units. 

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