Recursive algorithm for the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system

The connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system is included by the connected-X-out-of-(m, n):F lattice system defined by Boehme et al. [Boehme, T.K., Kossow, A., Preuss, W., 1992. A generalization of consecutive-k-out-of-n:F system. IEEE Transactions on Reliability 41, 451–457]. This system fails if and only if at least one subset of connected failed components occurs which includes at least a (1, 2)-matrix (that is, a row and two columns) or a (2, 1)-matrix(that is, two rows and a column) of failed components. This system is applied to two-dimensional network problems with adjacent constraints, and various systems, for example, a supervision system, etc.In this paper, we propose a new recursive algorithm for evaluating of the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system. We calculate the orders of the computing time and memory size of the our algorithm. We perform a numerical experiment in order to compare our proposed algorithm with the algorithm in the previous studies. A numerical experiment shows that the proposed algorithm is more efficient than the other algorithms for evaluating the reliability of the a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system when n is large.