Another difficulty in industrial experimentation is the existence of interactions. As has been stated, manufacturing processes are complex with many factors involved. In many processes these factors interact. This is particularly so for continuous processes such as plating or sputtering. Saying that the factors interact means more than that they are related to each other. It means that the effect of one (or more) factors on the response variable(s) changes when one (or more) other factor(s) changes its value.
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In order to detect interactions and understand the nature of their effects it is necessary to combine the interacting factors into the same experimental runs. The problem is not necessarily knowing in advance if the interactions exist. Sometimes they are predictable with theory. Sometimes they are discovered when the process behaves ’strangely’.

In addition to their efficiency, factorial designs also offer the only method of detecting interactions through experimentation. Because numerous factors can be combined in the same series of experimental runs, the interactions can be detected and the nature of their effects can be evaluated when they are present.