Stochastic ordering results for consecutive k-out-of-n:F systems

A linear (circular) consecutive k-out-of-n:F system is a system of n linearly (circularly) ordered components which fails if and only if at least k consecutive components fail. We use recursive relationships on the reliability of such systems with independent identically distributed components to show that for any fixed k, the lifetime of a (linear or circular) consecutive k-out-of-n:F system is stochastically decreasing in n. This result also holds for linear systems when the components are independent and not necessarily identically distributed, but not in general for circular systems.