In this paper, a new Fault Detection (FD) scheme based on combination of switching observer and Bond Graph (BG) method for linear continuous time switched systems with Average Dwell Time (ADT) approach is proposed. The proposed scheme is a BG-based two-stage FD system in which the compact state space representation and Global Analytical Redundancy Relations (GARRs) are derived based on the BG model. In the first stage, a switched observer is designed considering disturbance attenuation level, fault sensitivity and rapid fault detection criteria by solving a weighted Linear Matrix Inequality (LMI) optimization problem. Next, a new form of GARRs which is based on output estimation error of the observer and is called Error-based Global Analytical Redundancy Relations (EGARRs) is developed to combine the observer and BG method. The output estimation errors from the observer, which are adequately sensitive to faults and simultaneously the effects of disturbances are attenuated therein, are given to the EGARRs to generate the residuals of the FD system. The proposed method may be used for fault detection of switched linear systems with ADT based on the BG model of the system. Finally, two case studies including a two-tank system and a buck converter-driven DC motor are considered to show the efficiency and real-time implementation of the proposed method.