Reliability lower bounds for two-dimensional consecutive-k-out-of-n:F systems

The two-dimensional consecutive-k-out-of-n:F system has received extensive research interest due to the main fact that it can be applied into various areas, 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, we convert the two-dimensional consecutive-k-out-of-n:F system into a general one-dimensional consecutive-k-out-of-n:F system. Then, based upon the exact formula for the reliability of one-dimensional consecutive-k-out-of-n:F system, a simple formula is presented for the reliability lower bound of the two-dimensional consecutive-k-out-of- n:F system. Numerical results show the performance of the presented approach. In addition, it is shown that the proposed approach can be easily extended to t-within-connected-(r,s)-out-of-(m,n):F systems. An example is illustrated to derive the system reliability lower bounds.