Page 257 - Statistics for Environmental Engineers

L1592_Frame_C29 Page 261 Tuesday, December 18, 2001 2:48 PM

29

Screening of Important Variables

KEY WORDS confounding, constant variance, defining relation, fly ash, interactions, main effect, nor-
mal plot, permeability, factorial design, fractional factorial design, log transformation, replication, reso-
lution, variance.

Often, several independent variables are potentially important in determining the performance of a
process, or the properties of a material. The goal is to efficiently screen these variables to discover which,
if any, alter performance. Fractional factorial experiments are efficient for this purpose. The designs and
case study presented here are an extension of the factorial experiment designs discussed in Chapters 27
and 28.

Case Study: Using Fly Ash to Make an Impermeable Barrier

Fly ash from certain kinds of coal is pozzolanic, which means that it will set into a rock-like material
when mixed with proper amounts of water. Preliminary tests showed that pozzolanic fly ash can be
−7
mixed with sand or soil to form a material that has a permeability of 10 cm/sec or lower. Such mixtures
can be used to line storage lagoons and landfills if the permeability is not reduced by being frozen and
thawed, or wetted and dried. The effect of these conditions on the permeability of fly ash and sand/fly
ash mixtures needed to be tested. Two types of fly ash were being considered for this use. The addition
of a clay (bentonite) that has been frequently used to build impermeable barriers was also tested.
A two-level experiment was planned to evaluate the five factors at the levels listed below. The goal
was to formulate a durable mixture that had a low permeability.

1. Type of fly ash: A or B
2. Percentage of fly ash in the mixture: 100% ash, or 50% ash and 50% sand
3. Bentonite addition (percent of total mixture weight): none or 10%
4. Wet/dry cycle: yes or no
5. Freeze/thaw cycle: yes or no

5
A full two-level, five-factor experiment would require testing 2 = 32 different conditions. Each
permeability test would take one to three weeks to complete, so doing 32 runs was not attractive. Reducing
the number of variables to be investigated was not acceptable. How could five factors be investigated
without doing 32 runs? A fractional factorial design provided the solution. Table 29.1 shows the
5–1
experimental settings for a 16-run 2 fractional factorial experimental design.

Method: Designs for Screening Important Variables
k
A full factorial experiment using two levels to investigate k factors requires 2 experimental runs. The
k
data produced are sufficient to independently estimate 2 parameters, in this case the average (k main
k
effects) and 2 – k – 1 interactions. The number of main effects and interactions for a few full designs
are tabulated in Table 29.2.
© 2002 By CRC Press LLC