A study on reliability of a special two-dimensional system

A linear consecutive- (2, 2) -out-of-(m, n) : F system is a special two-dimensional system, which consists of m × n components, and fails if and only if all components in a 2 × 2 sub-matrix are failed. This system can be treated as a reliability model for video monitoring systems, phased-array radar systems, and wireless communication networks etc. An effective method has been developed for evaluating the exact system reliability, but that method can only give a recursive algorithm that can not be used for system optimization. In this paper, a finite Markov chain imbedding approach is used to obtain the reliability analytic formulas of that system. Numerical examples show that the method can be used for not only the system with independent identical distribution components, but also with independent non-identical distribution components.