A class of 2-step diagnosable systems: degree off diagnosability and a diagnosis algorithm

A diagnosability measure called t/-1-diagnosability is introduced. A system is t/-1-diagnosable if at least f-1 faulty units can be identified as long as the number of faulty units present, f, does not exceed t and the system is 1-fault diagnosable. This class of diagnosable systems is fully characterized. In addition, an O(n^3.5) diagnosis algorithm that locates at least f-1 faulty units when 1<f⩽t or the only faulty unit when f=1 is provided. When there is no faulty unit the algorithm certifies it. The algorithm is suited for any t/-1-diagnosable system