Consecutive -within--out-of-:F System with Nonidentical Components

Abstract

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