Typically sensors are placed at different locations that measure certain properties of the system at that location. Some properties that can be sensed include current, voltage, temperature etc. Because sensors are also physical devices and because of inherent uncertainty in data acquisition, the readouts from sensors can be noisy and may be incorrect if the sensors themselves have failed in some way.

Consider for example the network structure shown in Fig. \[fig:diagnosis\]a, consisting of a quaternary tree powered by a single battery source and with electrical current flowing down through intermediate CB nodes to the leaf sensor nodes. Suppose that the CBs and the ammeters might be faulty - affecting the propagation of current through the network and introducing uncertainty in the observation readouts, respectively. To simply the discussion, we assume in this report that the failure probability of the CBs is the same as the one for the ammeters. Under this assumption, the goal of the multiple-fault-diagnosis problem is to find the minimal number of faults, or broken electrical components (CBs and/or ammeters), that are consistent with the readout from the circuit. It is assumed here that power is generated only from this single node, and therefore will cause 