Linear <i>m</i>-Consecutive-<i>k</i>, <i>l</i>-Out-of-<i>n</i>: F System

Abstract

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 n 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.