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One-Factor-At-a-Time (OFAT) Experiments
Most experimental problems investigate two or more factors (independent variables). The most inefficient
approach to experimental design is, “Let’s just vary one factor at a time so we don’t get confused.” If
this approach does find the best operating level for all factors, it will require more work than experimental
designs that simultaneously vary two or more factors at once.
These are some advantages of a good multifactor experimental design compared to a one-factor-at-a-
time (OFAT) design:

• It requires less resources (time, material, experimental runs, etc.) for the amount of information
obtained. This is important because experiments are usually expensive.
• The estimates of the effects of each experimental factor are more precise. This happens
because a good design multiplies the contribution of each observation.
• The interaction between factors can be estimated systematically. Interactions cannot be esti-
mated from OFAT experiments.
• There is more information in a larger region of the factor space. This improves the prediction
of the response in the factor space by reducing the variability of the estimates of the response.
It also makes the process optimization more efficient because the optimal solution is searched
for over the entire factor space.

Suppose that jar tests are done to find the best operating conditions for breaking an oil–water emulsion
with a combination of ferric chloride and sulfuric acid so that free oil can be removed by flotation. The
initial oil concentration is 5000 mg/L. The first set of experiments was done at five levels of ferric
chloride with the sulfuric acid dose fixed at 0.1 g/L. The test conditions and residual oil concentration
(oil remaining after chemical coagulation and gravity flotation) are given below.

FeCl 3 (g/L) 1.0 1.1 1.2 1.3 1.4
H 2 SO 4 (g/L) 0.1 0.1 0.1 0.1 0.1
Residual oil (mg/L) 4200 2400 1700 175 650

The dose of 1.3 g/L of FeCl 3 is much better than the other doses that were tested. A second series of
jar tests was run with the FeCl 3 level fixed at the apparent optimum of 1.3 g/L to obtain:

FeCl 3 (g/L) 1.3 1.3 1.3
H 2 SO 4 (g/L) 0 0.1 0.2
Oil (mg/L) 1600 175 500

This test seems to confirm that the best combination is 1.3 g/L of FeCl 3 and 0.1 g/L of H 2 SO 4 .
Unfortunately, this experiment, involving eight runs, leads to a wrong conclusion. The response of oil
removal efficiency as a function of acid and iron dose is a valley, as shown in Figure 22.3. The first one-
at-a-time experiment cut across the valley in one direction, and the second cut it in the perpendicular
direction. What appeared to be an optimum condition is false. A valley (or a ridge) describes the response
surface of many real processes. The consequence is that one-factor-at-a-time experiments may find a
false optimum. Another weakness is that they fail to discover that a region of higher removal efficiency
lies in the direction of higher acid dose and lower ferric chloride dose.
We need an experimental strategy that (1) will not terminate at a false optimum, and (2) will point
the way toward regions of improved efficiency. Factorial experimental designs have these advantages.
They are simple and tremendously productive and every engineer who does experiments of any kind
should learn their basic properties.
We will illustrate two-level, two-factor designs using data from the emulsion breaking example. A
two-factor design has two independent variables. If each variable is investigated at two levels (high and
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