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/sup m-r//spl middot/m/sup 2//spl middot/r/spl middot/n) computing time. Comparisons with the existing methods show its usefulness. We prove that the reliability of the large system tends to exp(-/spl mu//spl middot//spl lambda//sup r/spl middot/s/) as n=/spl mu//spl middot/M/sup /spl eta/-1/, m/spl rarr//spl infin/ if every component has failure probability /spl lambda//spl middot/M/sup /spl eta//(r/spl middot/s/), where /spl mu/, /spl lambda/, /spl eta/ are constant, /spl mu/>0, /spl lambda/>0, /spl eta/>s, or r/(r-1)>/spl eta/>1.<
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