Derived from fullfactorial matrices

Using the assumption that all interactions are insignificant
relative to main factor effects, English statisticians Drs. Plackett
and Burman derived screening experiments matrices from
fullfactorial experiments matrices.

They took a basic threefactor, two level matrix and modified it
to reduce the confounding.

Main factor effects in PlackettBurman designs replace all
interactions of the full factorial matrix.

However, this does not mean that information about interactions
cannot be determined from PlackettBurman designs.
Screening experiments identify the “Power Factors” in a process.

Power factors are the process variables that most significantly
affect the process outputs, or responses.

In this unit, we cover the family of PlackettBurman screening
experiments that look at “f factors” in “f+1 treatment
combinations.”

Regardless of whether the experimental objective is to maximize
the response, minimize the response, or hit a target, the power
factors are the critical process or product variables used to adjust
and control the process or product output.
Plackett and Burman developed many designs.

Selection of the most appropriate design matrix will be determined
in large part by the number of factors selected for the
experimentation.

With an 8Run PlackettBurman design, we can look at up to 7
factors; with a 12Run design, up to 11 factors; with a 16Run
design up to 15 factors, and with a 20Run design, up to 19 factors.

The matrix that you select will depend on the number of factors to
be experimented upon plus the method chosen to determine the
experimental error.
There are several ways to determine the experimental error.

Among the options are:

Select the center point of the experimental levels and make
several experimental runs at that point;

Replicate the entire experimental matrix;

Make multiple independent measurements within a treatment
combination;

Use dummy factors; and

Use pooling. (Of these approaches, pooling is the least favored.)
Analyzing experimental results.

Once the experiment is run and the samples measured, the data from
the experiment are used to calculate the effects and to determine
the statistical significance of those effects.

Simply use the same matrix to analyze the experiment as was used
to set up and run it.

First, calculate the effects.

To calculate the effects, enter the average responses into the
matrix for each treatment combination.

Then, working with the columns, determine the effect, which is the
difference between the average response at the high level and the
average response at the low level. Using the signs in the column,
add up the responses and then divide by the number of pluses.

Take care to note the sign of the effect.

The effect for a factor is always described as the change in the
response in going from the low level of that factor to the high
level.

A negative sign means that going from low level to high level for
a factor decreases the response.

A positive sign means that going from the low level to the high
level increases the response.

Remember the experimental objective.

Determining which levels to set the factors at depends on the
experimental objective.

If the goal is to maximize a response, then all factors with a
positive effect would be set to operate at their high levels and all
factors with a negative effect would be set to operate at their low
levels.

If the objective was to minimize the response, then all factors
with a positive effect would be set at low levels and all with a
negative effect would be set at high levels.

If the goal was to be closest to target, then the effects will be
used to determine how to change factor levels to dial in the
process.

Is the effect statistically significant?

There is no way to know if the effects are due to changes made in
the factor levels or due to common cause variation in the process
unless their statistical significance is tested.

If an effect does test to be statistically significant, the
associated factor is a power factor.

