On Models for Diagnosable Systems and Probabilistic Fault Diagnosis

This paper is concerned with automatic fault diagnosis for digital systems with multiple faults. Three problems are treated: 1) Probabilistic fault diagnosis is presented using the graph-theoretic model of Preparata et al. The necessary and sufficient conditions to correctly diagnose any fault set whose probability of occurrence is greater than t have been developed. Some simple sufficient conditions are also discussed. 2) A general model that contains as special cases both the graph-theoretic and the Russell-Kime models is developed. Conditions for T-fault diagnosability are given, thus settling some open problems introduced by Russell and Kime. 3) Finally, sequential T-fault diagnosability is considered. Existence of a class of systems requiring as little as n + T - 1 tests is shown. This improves significantly upon the previously best known class of systems that required n + 2T - 2 tests for sequential T-fault diagnosability.