Linear $m$ -Consecutive-$k$ , $l$-Out-of-$n$: F System

We propose a new model which generalizes the linear m-consecutive-k-out-of-n:F system to the case of the m-consecutive-k-out-of-n:F system with l-overlapping runs. The new system is called the m-consecutive-k, l-out-of-n:F system, and consists of linearly ordered components such that the system fails iff there are at least m l-overlapping runs of k consecutive failed components. The number of path sets including a specified number of working components is obtained via a combinatorial method, and this quantity is used to obtain the reliability and the signature of the system.