LOWER AND UPPER-BOUNDS FOR THE RELIABILITY OF CONNECTED-(R,S)-OUT-OF-(M,N)-F LATTICE SYSTEMS

A linear (m,n)-lattice system is a system whose components are ordered like the elements of a (m,n)-matrix. A circular (m,n)-lattice system is a system whose components are represented by the junctions of m cir cles centered at the same point and n beams starting from that point a nd crossing the circles (the circles and the beams are not necessarily physical objects), It is assumed that in both lineal & circular cases , the components have only two states: 1 (operating) and 0 (failed). A linear/circular connected-(r,s)-out-of-(m,n):F lattice system is a li near/circular (m,n)-lattice system that fails if at least 1 connected (r,s)-submatrix of failed components occurs. The paper gives lower & u pper bounds for the reliabilities of such systems.