Diagnosability and Distinguishability Analysis and Its Applications

As systems become more complex, it becomes necessary to understand, simplify, and apply fault diagnosis and fault-tolerant design. Although some graph-theoretical diagnostic models such as self-diagnosis model have been studied, the model can not be applied to most systems due to the assumption that each unit has its own testing capability. This paper presents a graph-theoretical diagnosis model expressed by a set of fallible units, a set of measurements, and an incident matrix indicating binary relation between these two sets. Since this model explicitly separates tested units (fallible units) and testing units (measurements), we can discuss diagnostic aspects from both sides. Diagnosability and distinguishability of the model with multiple faults are discussed from combinatorial point of view. Measures of t-fault diagnosability and t-out-of-s diagnosability which was introduced on the self-diagnosis model are discussed. Conditions for these diagnosabilities are expressed by a topological concept of fault distance. The concept of distinguishability is generalized to multiple fault situations called t-fault distinguishability. A lower bound for the distinguishability is obtained by using fault distance. The new concept of s-distinguishability class (s-dc) is presented. This analysis is recommended in the design of systems to attain a required level of diagnosability and distinguishability as well as in the analysis of present systems to investigate their diagnostic aspects. Two application examples are presented: Diagnosability and distinguishability analysis of error-correcting codes, and design of instrumentation systems of large plants with a required level of diagnosability.