This paper presents an adaptive Generalized Likelihood Ratio (GLR) test for multiple Faults Detection and Isolation (FDI) in stochastic linear dynamic systems. Based on the work of Willsky and Jones (1976), we propose a modified generalized likelihood ratio test, allowing detection, isolation and estimation of multiple sequential faults. Our contribution aims to maximise the good decision rate of fault detection using another updating strategy. This is based on a reference model updated on-line after each detection and isolation of one fault. To reduce the computational requirement, the passive GLR test will be derived from a state estimator designed on a fixed reference model directly sensitive to system changes. We will show that active and passive GLR tests will be mixed and give interesting results compared with the GLR of Willsky and Jones (1976), and that they can be easily integrated in a reconfigurable Fault-Tolerant Control System (FTCS) to asymptotically recover the nominal system performances of the jump-free system.