A Generalization of Diagnosability Analysis

Abstract

A new concept of generalized diagnosability is proposed for a formal diagnosis model which incorporates most diagnosis models so far proposed. A self-diagnosis model consists of a set of units which can test other units and be tested by other units. Generalized diagnosability is a new measure of diagnosability in system diagnosis problems which is extensively studied with respect to self-diagnosis models. This diagnosability expresses explicitly such information as (1) the maximum number of units to be identified as faulty, (2) the maximum number of units to be identified as fault-free, and (3) the maximum number of units whose states are definitely identified when the upper bound on the number of faulty units is assumed. Conditions for generalized diagnosability are expressed by certain relations between the power sets of a set of faulty units. Since these conditions are of the form that they must be checked all over the possible syndrome, it is generally difficult to investigate generalized diagnosability. However, these conditions are meaningful in cases in which the graph of a diagnosis model has symmetricity, or a diagnosis model has a constrained structure about the relation between fault patterns and syndromes. Some examples of these cases are presented. Furthermore, we discuss the problem of finding the minimal fault pattern consistent with a given syndrome. This problem is formulated as a mathematical programming problem with the same relations both in constraints and objective functions as those used to express conditions for generalized diagnosability.