Far East Journal of Theoretical Statistics
Volume 18, Issue 2, Pages 193 - 203
(March 2006)
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STOCHASTIC ORDERING RESULTS FOR m-CONSECUTIVE-k-OUT-OF-n:
F SYSTEMS
Boushaba Mahmoud (Algeria) and Azouz Zineb (Algeria)
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Abstract: A linear (circular) "m-consecutive-k-out-of-n:
F system" is a system of n linearly (circularly) ordered
components which fails if and only if at least m non-overlapping runs of k
consecutive components fail. We use recursive relationships for the reliability
of such system with independent identically distributed components to show that
for any fixed k and m, the lifetime of a (linear or circular) m-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. |
Keywords and phrases: linear and circular m-consecutive-k-out-of-n:
F systems, stochastic order, system reliability. |
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