Reliability of Combined Consecutive out of F and Consecutive out of F Systems

摘要

A combined $m$ -consecutive-$k$ -out-of-$n$ :F & consecutive-$k_{c}$ -out-of-$n$ :F system consists of $n$ linearly ordered components, and fails iff there exist at least $k_{c}$ consecutive failed components, or at least $m$ non-overlapping runs of $k$ consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components.