Active fault detection for a stable open-loop LTI SISO system is considered. The optimal active fault detection setup is developed around an estimator based architecture. The auxiliary signal and estimator are then designed in order to maximize detection performance. Equations are derived which relate the estimator design to the nominal residual signal covariance. The relationship between the auxiliary input and the system performance degradation constraint is considered. The effect of estimator gain and excitation signal frequency on the dual Youla-Jabr-Bongiorno-Kucera parameter is investigated. Finally, the effect of the excitation signal frequency on detector performance is investigated, and a minimum targeted detection time parameter is introduced. This set of equations are then used to minimise the fault detection time for fixed performance constraints and minimum targeted detection time.