Computation of Diagnosable Fault-Occurrence Indices for Systems with Repeatable-Faults

We study discrete-event systems prone to such faults which can occur repeatedly. For the diagnosis of re- peatable faults, [5] introduced the notion of l-diagnosability requiring the diagnosis of the lth occurrence of a fault within a bounded delay. The present paper studies the identification of the set of all indices a for which the system is l-diagnosable. (These are precisely the occurrence indices for which a repeatable-fault can be diagnosed.) We first present a test to verify whether a fault is diagnosable for each occurrence index, i.e., whether it is “∀l-diagnosable”. For systems that fail this test, we further present a method to compute the set of all indices l for which the system is not l-diagnosable.