On the Lifetime Distribution of Consecutive K-Out F System

Abstract

A consecutive k-out-of-n : F system is a system of n components which fails iff k consecutive components fail. In this paper, we consider the lifetime of consecutive k-out-of-n : F systems and provide some stochastic ordering results. It is shown that the usual stochastic ordering is preserved under the formation of consecutive k-out-of-n : F systems of s-independent, nonidentical, and exchangeable components. A counter example is also given to show that the mean residual life ordering is not, in general, preserved by a consecutive k-out-of-n : F system.