Abstract: Concurrent error detection is important for improving dependability of digital circuits and systems. In this paper, a structure module for basic concurrent error detection circuit is built. It is constructed by a basic functional module and a detector. Several new concepts, reduced strongly fault secure, reduced strongly variable disjoint, reduced strongly self checking, k fault tolerant reduced strongly fault secure, k fault tolerant reduced strongly variable disjoint, and k fault tolerant reduced strongly self checking are defined to characterize circuits with partially self checking capability. The relations among all of these concepts about concurrent error detection are presented. Interconnection conditions, with which the basic functional modules and detectors must satisfy to construct basic circuits with different concurrent error detection properties, are proved.