DOE is much more effective if the process is stable ... in a state of statistical control. To show that a process is 'stable' requires an SPC-based study, which would include some type of charting method (X-bar and R, other).
If the process behavior is erratic, it is possible that any DOE efforts will be less effective, and possibly a waste of time and resources.
HOWEVER ... even though a process may not be a state of 'perfect' statistical control (and what process is?), this does not mean that further exploration and study of the process is not warranted. This depends on the nature and extent of the process instability, and the resulting impact on any related studies (DOE, other).