A new method for fault detection and isolation (FDI) in stochastic linear time varying (LTV) systems is proposed in this paper. It allows to completely isolate any number of faults regardless of the number of output sensors, thanks to an appropriate assumption on the fault profiles and to some persistent excitation condition. In contrast, most existing methods enabling complete fault isolation have been developed for linear time invariant (LTI) systems and require a strong condition on the number of sensors. The method proposed in this paper is based on a recent development for the design of adaptive observers. Its performance is illustrated by a numerical example.