The design of a high-gain observer-based residual is considered for a class of non-linear systems. Input - output maps are derived for use in residual design to increase design flexibility. An investigation is performed on two different application systems to compare and test the effectiveness of designed residuals. For each of the two application systems, of chosen dimension ( starting with low dimension), residual performances are compared for different fault types, fault magnitudes and fault positions. Performances are compared for different dimensions of application system. Both qualitative and quantitative evidence is collected to show that residual effectiveness can degrade in several ways and in a non-linear manner. The latter is shown to be exhibited by certain logarithmic curves.