Coherent Systems in Profust Reliability Theory

Profust reliability theory is based on the probability assumption and the fuzzy-state assumption. In an attempt to provide a uniform foundation for profust reliability theory, in this paper we introduce the concept of coherent systems and distinguish two classes of systems: closely coherent systems and loosely coherent systems. To formulate the relationships between system reliabilities and component reliabilities, we present a number of general results, results concerning convexity, and results concerning unimodality. It is argued that for a coherent system, component reliability improvements don’t certainly enhance the system reliability.