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

A circular connected-(r, s)-out-of-(m, n): F lattice system has m . n components and is consisted of n rays and m circles. The system fails if and only if a connected (r, s)-matrix of components fail. Firstly, this paper proposes a recursive algorithm for the reliability of the system, which requries computing time. In the statistically independent identically distributed case, the computing time is able to be reduced. Secondly, the upper and lower bounds for the system reliability are obtained for the circular connected-(r, s)-out-of-(m, n): F lattice system. Finally, it is proved that the reliability of the large system tends to as , if every component has failure probability , where , and are constant,,.