Abstract
A connected-(r,s)-out-of-(m,n):F lattice system consists of components arranged as an (m,n) matrix, and fails if and only if the system has an (r,s) sub-matrix where all components fail. Though the previous study has proposed the recursive equation for computing the system reliability, it takes much time to compute the reliability. For one-dimensional systems, a matrix formula was provided based on the existing recursive equation when the system consists of independent and identically distributed components. The numerical experiments showed that the matrix formula was more efficient than the recursive equation. In contrast, for two-dimensional systems, the recursive equation is comparatively complex, so that it is difficult to drive a matrix formula directly from the recursive equation. In this study, we derive general forms of matrices for computing the reliability of the connected-(r,s)-out-of-(m,n):F lattice system consisting of independent and identically distributed components in the case of and . We compare our proposed method with the recursive equation in order to verify the effectiveness of the proposed method using numerical experiments.
Highlights
The recursive equation is based on the event decomposition approach (Kuo et al, 2002), and we can calculate the system reliability when the components are Independent but Non-Identically Distributed (INID)
Lin (2004) provided a matrix formula for computing the reliability of the system consisting of Independent and Identically Distributed (IID) components based on the recursive equations of Hwang (1982)
As an extension to two-dimensional systems, if we obtain matrices for computing the system reliability based on the recursive equation of Yamamoto and Miyakawa (1995), we can compute the reliability of the connected-(r,s)-out-of-(m,n):F lattice system
Summary
Systems of modern societies such as communication systems and electricity supply systems have a significant number of components, and the components have complicated relationships. Lin (2004) provided a matrix formula for computing the reliability of the system consisting of Independent and Identically Distributed (IID) components based on the recursive equations of Hwang (1982). As an extension to two-dimensional systems, if we obtain matrices for computing the system reliability based on the recursive equation of Yamamoto and Miyakawa (1995), we can compute the reliability of the connected-(r,s)-out-of-(m,n):F lattice system. The aim of this paper is to derive general forms of matrices for computing the reliability of the connected-(r,s)-out-of-(m,n):F lattice system consisting of IID components in the case of r m 1 and r m 2 , and compute the reliability with the fast-matrix-power algorithm. 3. Matrix Approach for the Reliability we provide matrices to obtain the reliability of the connected-(r,s)-out-of-(m,n):F lattice systems consisting of IID components.
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