Expected-value analysis of two single fault diagnosis algorithms

The problem of diagnosing single faults is addressed for systems whose fault propagation properties can be modeled as directed graphs. In these systems, the nodes represent components and the edges represent fault propagation between the components. Some of the components are equipped with alarms that become active in response to faulty conditions. Two algorithms FORWARD and BACKWARD for computing the set of all potential candidates for a single fault that corresponds to given set of active alarms, are studied. The algorithm FORWARD moves forward from candidate nodes checking to see if they satisfy the alarm condition, and the algorithm BACKWARD moves backward from the alarms. In terms of worst-case time complexity the algorithm BACKWARD is better. These two algorithms are analyzed using systems that are uniformly and randomly generated. In terms of the expected number of distinct nodes that are visited, the algorithm FORWARD is shown to be better, and in terms of the total number of node visits the algorithm BACKWARD is found to be better. Thus these algorithms are suited for different modes of storing the system graph.