Based on fault dictionary technique and discrete event system (DES) off-line diagnosis model, a new approach called state partition (SP) technique was proposed to model the mixed-circuit in an unified way. Mathematic analysis was made the main part with relationship between system states and state partitions concerned specially. The definition of "cross intersection" was given, and the operation of cross intersection was proved close and to be a conjunction of the partition set. With the idea mentioned in DES off-line diagnosis model, the concept of system diagnosability was built. The existence and reachability of minimal phenomenon set were also proved in SP model. To locate system status, phenomena were used to divide state set into partitions. So fault dictionary technique and DES off-line diagnosis model are unified theoretically from math aspect in relation between state and its partitions. SP model is also proved a universal method in circuit fault diagnosis.