Statistics for Environmental Engineers

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(a)



Time


Pressure

Temperature



One-factor-at-a time design in 13 runs



FIGURE 22.5 Graphical demonstration of why one-factor-at-a-time (OFAT) experiments cannot estimate the two-factor interaction between temperature and pressure that is revealed by the two-level, two-factor design.

design in 8 runs


Box-Behnken design in three factors in 13 runs


Composite two-level, 3-factor design in 15 runs



a>



0.



Yield = 11



10



7



Temperature



12


optional 7


Temperature



Yield = 11



2



>-



New


pressure



n


TO



New pressure




Standard


pressure



>-



Standard


pressure



_i_i_


Standard New Temperature



Standard New Temperature



One-Factor-at-a Time Experiment



Two-level Factorial Design Experiment


FIGURE 22.6 Four possible experimental designs for studying three factors. The worst is (a), the one-factor-at-a-time design (top left). (b) is a two-level, three-factor design in eight runs and can describe a smooth nonplanar surface. The Box-Behnken design (c) and the composite two-level, three-factor design (d) can describe quadratic effects (maxima and minima). The Box-Behnken design uses 12 observations located on the face of the cube plus a center point. The composite design has eight runs located at the corner of the cube, plus six “star” points, plus a center point. The corner and star points are equidistant from the center (i.e., located on a sphere having a diameter equal to the distance from the center to a corner).


It is generally true that (1) the factorial design gives better precision than the OFAT design if the factors do act additively; and (2) if the factors do not act additively, the factorial design can detect and estimate interactions that measure the nonadditivity.

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