Reliability Function of the Connected-(2,2)-out-of-(m,n): F Linear and Circular System Using Markov Chain

The two-dimensional connected-(2,2)-out-of-(m,n): F linear (circular) system consists of m x n components and fails if and only if there is at least a 2 x 2 square that contains all failed components. This paper proposed a new approach to imbed the system in a Markov chain in order to compute the reliability. The states of the Markov chain were derived using the working and the failure states of the one dimensional consecutive 2-out-of-n: F linear (circular) system. Illustrative example of the system was provided with independent identical distribution components, but it is also applied for the independent non-identical distribution components.