m‐consecutive‐k‐out‐of‐n:F system with overlapping runs: signature‐based reliability analysis

Consecutive‐k‐out‐of‐n system and its generalisations have attracted substantial interest due to their applications to model telecommunications systems, oil pipeline systems, heating systems, etc. One of the most important generalisation of this system is an m‐consecutive‐k‐out‐of‐n:F system. An m‐consecutive‐k‐out‐of‐n:F system with overlapping runs is a system consisting of n linearly ordered components and fails if and only if there are at least m overlapping runs of k consecutive failures. For m = 1, the system is same with the usual consecutive‐k‐out‐of‐n:F system. In this paper, we study the reliability properties of such systems via system signature. In particular, we obtain a closed form expression for the signature of this system and use it to compute and evaluate several reliability characteristics of the system.