Consecutive <i>k</I>-within-<i>m< System With Nonidentical Components

Abstract

As a generalisation of consecutive k-out-of-n:F and k-out-of-n:F system models, a consecutive k-within-m-out-of-n: F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. In this paper, we study the survival function of a consecutive k-within-m-out-of-n:F system consisting of independent but nonidentical components. We obtain exact expressions for the survival function when 2m >= n. A detailed analysis for consecutive 2-within-m-out-of-n:F systems is presented and the asymptotic behaviour of hazard rate of these systems is investigated using mixture representations.