The Rationale of Scientific Experimentation by John Dowd explains the value of designed experiments.
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.
The paper also explains analytic and enumerative studies. Dr. Deming stressed the importance of understanding the distinction between the two.