On the Lifetime Distribution of Consecutive k-out-of-n:F System

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