## Related questions with answers

Construct a Plackett-Burman design for 10 variables containing 24 experimental runs.

Solution

VerifiedBecause we have 24 experimental runs, which means that we have 24 design points ($N=24$), we have the following basic line.

$\begin{align*} +++++-+-++--++--+-+---- \end{align*}$

The previous basic line will be in the first column.

On the the top of the second column will be the sign from the bottom of the first column, and then one after the other signs from the first column from the first to the penultimate.

On the the top of the third column will be the sign from the bottom of the second column, and then one after the other signs from the second column from the first to the penultimate, and so on.

In this exercise we will have 10 columns, because we have 10 variables.

We can conclude that in each column we have 23 signs, and we need 24, because we have 24 design points.

Because of that, at the end we fill in the last row with negative signs.

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