Bounds for coherent reliability structures

Esary and Proschan (1963) proposed a lower bound (resp. upper bound) for the reliability of a general coherent system, which was expressed via system's minimal cut (resp. path) sets. In this article we provide a lower bound based on the minimal path sets and an upper bound based on the minimal cut sets. These bounds, which include as a special case the bounds derived recently by Fu and Koutras (1994b), are subsequently used for the efficient reliability approximation of various coherent structures.