Multivariate statistical approaches to Fault detection based on historical operating data have been found to be useful with processes having a large number of measured variables and when causal models are unavailable. For fault isolation or diagnosis they have been less powerful because of the non-causal nature of the data on which they are based. To improve the fault isolation with these methods. additional data on past faults have been used to supplement the models. A critical review of this fault isolation literature is given. and an improved approach capable of handling both simple and complex faults is presented. This approach extracts fault signatures that are vectors of movement of the fault in both the model space and the residual space. The directions of these vectors are then compared to the corresponding vector directions of known faults in the fault library. Isolation is then based on a joint plot of the angles between the vectors of the current fault and those of the known faults. Although the fault signatures are based on steady-state information, the methodology assumes that time varying disturbances due to common-cause sources are always present, and it is applied to dynamic data as soon as a fault is detected. The method is demonstrated using a simulated CSTR system with feedback control, and is shown to be effective in isolating both simple and complex faults.