Networks, mainly composed of cables, are prone to failures. Faults in cables are initially benign (so-called soft faults) and then evolve over time to a much more severe form of faults as short or open circuits (so-called hard faults). It is thus of prime importance to detect and localize efficiently the soft faults. Residuals may be calculated by comparing online computed transmission coefficients with reference transmission coefficients. In this paper, the sensitivity of the residuals with respect to the fault is studied for a simulated but realistic Yshaped network. The residuals are represented in the residual space. Using intensive simulations, the residuals are analyzed with respect to the position of the fault in a branch, the severity of the fault and the signal-to-noise ratio.