Abstract—A linear (circular) consecutive k-out-of-n Fsystem
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 systemswhenthe components are independent and not necessarily
identically distributed, but not in general for circular systems.
Index Terms—Linear and circular consecutive -out-of- systems,
stochastic order, system reliability.
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