Page 194 - Statistics for Environmental Engineers

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Initial Design

Augment Change
the Design Settings
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Check Replicate Relocate Rescale
quadratic
effects
FIGURE 22.7 Some of the modifications that are possible with a two-level factorial experimental design. It can be stretched
(rescaled), replicated, relocated, or augmented.
of interactions as well as the effects of changing the three factors. Figure 22.6b is a two-level, three-
factor design in eight runs that 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. There are advantages to setting the corner and star points equidistant from the center (i.e., on a
sphere having a diameter equal to the distance from the center to a corner).
Designs (b), (c), and (d) can be replicated, stretched, moved to new experimental regions, and expanded
to include more factors. They are ideal for iterative experimentation (Chapters 43 and 44).

Iterative Design

Whatever our experimental budget may be, we never want to commit everything at the beginning. Some
preliminary experiments will lead to new ideas, better settings of the factor levels, and to adding or
dropping factors from the experiment. The oil emulsion-breaking example showed this. The importance
of iterative experimentation is discussed again in Chapters 43 and 44. Figure 22.7 suggests some of the
iterative modifications that might be used with two-level factorial experiments.

Comments

A good experimental design is simple to execute, requires no complicated calculations to analyze the
data, and will allow several variables to be investigated simultaneously in few experimental runs.
Factorial designs are efficient because they are balanced and the settings of the independent variables
are completely uncorrelated with each other (orthogonal designs). Orthogonal designs allow each effect
to be estimated independently of other effects.
We like factorial experimental designs, especially for treatment process research, but they do not solve
all problems. They are not helpful in most field investigations because the factors cannot be set as we
wish. A professional statistician will know other designs that are better. Whatever the final design, it
should include replication, randomization, and blocking.
Chapter 23 deals with selecting the sample size in some selected experimental situations. Chapters
24 to 26 explain the analysis of data from factorial experiments. Chapters 27 to 30 are about two-level
factorial and fractional factorial experiments. They deal mainly with identifying the important subset of
experimental factors. Chapters 33 to 48 deal with fitting linear and nonlinear models.

© 2002 By CRC Press LLC