The detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed. A cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test. For input design, the objectives are taken to be to decrease the detection time and, at the same time, to ensure a tolerable false alarm rate. Both off-line auxiliary inputs and on-line generation of the input signal by a linear output feedback are considered. The problem is first introduced for the two-hypotheses case and then the design techniques are extended to the general multiple-hypotheses case.