The major types of Designed Experiments are:
Full Factorials

As their name implies, full factorial
experiments look completely at all factors
included in the experimentation.

In full factorials, we study all of the
possible treatment combinations that are
associated with the factors and their levels.
They look at the effects that the main factors
and all the interactions between factors have on
the measured responses.

If we use more than two levels for each
factor, we can also study whether the effect on
the response is linear or if there is curvature
in the experimental region for each factor and
for the interactions.

Full factorial experiments can require many
experimental runs if many factors at many levels
are investigated.
Fractional Factorials

Fractional factorials look at more factors
with fewer runs.

Using a fractional factorial involves making a
major assumption  that higher order
interactions (those between three or more
factors) are not significant.

Fractional factorial designs are derived from
full factorial matrices by substituting higher
order interactions with new factors.

To increase the efficiency of experimentation,
fractional factorials give up some power in
analyzing the effects on the response.
Fractional factorials will still look at the
main factor effects, but they lead to
compromises when looking into interaction
effects.

This compromise is called confounding.

Just because we have confounded main factor
and interaction effects doesn’t mean fractional
factorials are a poor choice. The risks we are
taking are well worth it.

Threeway and higher interactions are rare and
even twoway interactions are not that
commonplace. The efficiency in experimentation
more than makes up for the confounding of
results that we get.
Screening Experiments

Screening experiments are the ultimate
fractional factorial experiments. These
experiments assume that all interactions, even
twoway interactions, are not significant.

They literally screen the factors, or
variables, in the process and determine which
are the critical variables that affect the
process output.

There are two major families of screening
experiments:

Drs. Plackett and Burman developed the
original family of screening experiments
matrices in the 1940s.

Dr. Taguchi adapted the Plackett–Burman
screening designs. He modified the Plackett–Burman
design approach so that the experimenter could
assume that interactions are not significant,
yet could test for some twoway interactions at
the same time.
Response Surface Analysis

Response surface analysis is an offline
optimization technique. Usually, 2 factors are
studied; but 3 or more can be studied.

With response surface analysis, we run a
series of full factorial experiments and map the
response to generate mathematical equations that
describe how factors affect the response.
EVOP

EVOP (evolutionary operations) is an online
optimization technique.

Usually, two factors are studied using small,
step changes in factor levels to incrementally
explore the operating bounds of the process.
Mixture Experiments

The designs we have looked at so far work fine
for variables like temperature, pressure, or
time and even for material substitutions. But
they will not work in situations where we need
to study how changes in the formulation affect
the final properties of a material.

When dealing with formulations, there are
added constraints on the experimenter. When
dealing with composition, the sum of all of the
weight fractions of all the components must add
up to 1.0 and each of the individual components
must have a weight fraction between 0 and 1.0.
Mixture experiments provide techniques to
operate within these constraints.
Experimental Strategy

When setting up an experimental strategy, it
is usually best to start with screening
experiments to separate out the important
(significant) factors from the many factors in a
process.

From there we can experiment further on the
significant factors and study their interactions
with fractional factorial or full factorial
experiments.

In some cases, once we have identified the
power factors, we may want to optimize the
response using the power factors in one of the
two major DOE techniques for optimizing
processes, Response Surface Analysis or EVOP.

