A recursive algorithm for the 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 consists of m×n components arranged in a cylindrical grid. Each of m circles has n components, and this system fails if and only if there exists a grid of size r ×s which all components are failed. A circular connected-(r, s)-out-of-(m, n):F lattice system might be used in reliability models for ‘Feelers for measuring temperature on reaction chamber’ and ‘TFT Liquid Crystal Display system with 360° wide area’. In this study, we proposed a new recursive algorithm for obtaining the reliability of a circular connected-(r, s)-out-of-(m, n):F lattice system. We evaluated our proposed algorithms in terms of computing time and memory capacity. Furthermore, a numerical experiment comparing our proposed algorithm with Yamamoto and Miyakawaʹs algorithm [Yamamoto, H., & Miyakawa, M. (1996). Reliability of circular connected-(r, s)-out-of-(m, n):F lattice system. Journal of the Operations Research Society of Japan, 39(3), 389–406] showed that our proposed algorithm is more effective for systems with a large n.