Reliability lower bounds for two-dimensional consecutive-\(k\)-out-of-\(n\): F systems
A new system, namely consecutive-\(k\)-out-of-\(n\) : F system (or (one-di\-men\-si\-o\-nal) \(C(k,n : F)\) system), has caught much attention since 1980 [\textit{M. T. Chao, J. C. Fu, M. V. Koutras} [IEEE Trans. Reliab. 44, 120--127 (1995)]) due to the followings: \(C(k,n : F)\) system usually has much higher probability than the series system, and is less expensive than the parallel systems. The \(C(k,n : F)\) system consists of \(n\) linearly connected components, and it fails iff there are consecutive \(k\) or more than \(k\) components failed. Two-dimensional \(C(k,n : F)\) systems have received extensive research interest due to the main fact that it can be applied into various areas in the real world, e.g., safety monitoring systems, design of electronic devices, disease diagnosis, and pattern recognition. As known, recursive algorithms can be used to derive the exact system reliability. However, the computing time complexity is exponential and it is infeasible for larger systems. In this paper, with the use of ``artificial perfect components'', the authors successfully convert a two-dimensional \(C(k,n : F)\) system into a one-dimensional \(C(k,n : F)\) system. Then, based upon the exact formula for obtaining the better reliability of one-dimensional \(C(k,n : F)\) system, a simple formula is presented for the reliability lower bound of the two-dimensional \(C(k,n : F)\) system. Numerical results show the performance of the presented approach. In addition, the authors show that the proposed approach can be extended to the more general \(t\)-within-connected-\((r,s)\)-out-of-\((m,n)\) : F systems. An example shows the performance of the reliability lower bounds. The proposed technique could be useful for system designers and researchers in estimating the reliability lower bounds for \(t\)-within-connected-\((r,s)\)-out-of-\((m, n)\) : F systems.
consecutive-\(k\)-out-of-\(n\) : F system
scientific article; zbMATH DE number 2115373