Statistics for Environmental Engineers

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C (g/L)


D (1/h)


R(g/h)


0.5


0.14


0.018


0.5


0.16


0.025


1.0


0.14


0.030


1.0


0.16


0.040

Phenol Concentration (mg/L)


FIGURE 43.2 Response surface computed from the data collected in exploratory stage 1 of the optimizing experiment.

Second Iteration


Design — The first iteration indicates a promising direction but does not tell us how much each setting should be increased. Making a big step risks going over the peak. Making a timid step and progressing toward the peak will be slow. How bold — or how timid — should we be? This usually is not a difficult question because the experimenter has prior experience and special knowledge about the experimental conditions. We know, for example, that there is a practical upper limit on the dilution rate because at some level all the bacteria will wash out of the reactor. We also know from previously published results that phenol becomes inhibitory at some level. We may have a fairly good idea of the concentration at which this should be observed. In short, the experimenter knows something about limiting conditions at the start of the experiment (and will quickly learn more). To a large extent, we trust our judgment about how far to move.


The second factor is that iterative factorial experiments are so extremely efficient that the total number of experiments will be small regardless of how boldly we proceed. If we make what seems in hindsight to be a mistake either in direction or distance, this will be discovered and the same experiments that reveal it will put us onto a better path toward the optimum.

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