Self-Implicating Structures for Diagnosable Systems

In this paper, a new class of diagnosable systems, called tp-self-implicating systems, which is a special case of the well-known tp-diagnosable systems introduced by Preparata et al. [1], is described. If there are no more than tp faulty units and the faults are assumed to be permanent, then the faulty units in a tp-self-implicating system can always be identified using at least one of two straight forward criteria associated with test outcomes. In each case, the given faulty unit in effect implicates itself as faulty. Necessary and sufficient conditions are given on the structures of PMC models for self-implication. Finally, an algorithm for identifying the set of faulty units in a tp-self-implicating system is given which is linear in the number of tests in the system, rendering it more efficient than the most efficient known algorithm for the general class of tp-diagnosable systems.