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Model-based fault diagnosis, using statistical techniques, residual generation (by analytical redundancy), and parameter estimation, has been an active area of research for the past four decades. However, these techniques are developed in isolation and generally a single technique can not address the diagnostic problems in complex systems. In this paper, we will investigate a hybrid approach, which combines different techniques to obtain better diagnostic performance than the use of a single technique alone, and demonstrate it on an Anti-lock Brake System. In this approach, we first combine the parity equations and nonlinear observer to generate the residuals. Statistical tests, in particular Generalized Likelihood Ratio tests (GLRT), are used to detect a subset of faults that are easier to detect. Support Vector Machines (SVM) are used for fault isolation of less-sensitive parametric faults. Finally, subset selection for improved parameter estimation is used to estimate fault severity.