Reliability of a 2-dimensional k-within-consecutive-r x s-out-of-m x n : Fsystem

A 2-dimensional rectangular (cylindrical) k-within-consecutive-r x s-out-of -m x n:F system is the rectangular (cylindrical) m x n-system if the system fails whenever k components in a r x s-submatrix fail. This paper proposes a recursive algorithm for the reliability of the 2-dimensional k-within-co nsecutive-r x s-out-m x n:F system, in the rectangular case and the cylindr ical case. This algorithm requires min(O(mk(r(n-s))), O(nk(s(m-r)))), and O (mk(rn)) computing time in the rectangular case and the cylindrical case, r espectively. The proposed algorithm will be demonstrated and some numerical examples will be shown. (C) 2001 John Wiley & Sons, Inc.