This thesis is concerned with the automatic fault diagnosis for systems with multiple faults. A system consists of n units and each unit is capable to test other units.
We consider two-step t-diagnosable systems. A system S is called two-step t-diagnosable if by no more than two applications of the diagnostic tests, all faulty units in S can be diagnosed and repaired provided the number of faulty units does not exceed t. Some necessary conditions and some classes of two-step t-diagnosable systems are given. And optimal design of two-step t-fault diagnosable systems is presented.