Reliability of a linear connected-(r,s)-out-of-(m,n):F lattice system

A linear connected-(r,s)-out-of-(m,n):F lattice system has its components ordered like the elements of a (m,n)-matrix such that the system fails if all components in a connected (r,s)-submatrix fail. This paper proposes a recursive algorithm, named Yamamoto-Miyakawa (YM), for the system reliability. The YM algorithm requires O(s^m-r·m²·r·n) computing time. Comparisons with the existing methods show its usefulness. We prove that the reliability of the large system tends to exp(-μ·λ^r·s) as n=μ·M^η-1, m→∞ if every component has failure probability λ·M^η(r·s/), where μ, λ, η are constant, μ>0, λ>0, η>s, or r/(r-1)>η>1