Signature based analysis of m-Consecutive-k-out-of-n: F systems with exchangeable components

In this article, we study reliability properties of m‐consecutive‐k‐out‐of‐n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the...

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Bibliographic Details
Published in:Naval research logistics 2011-06, Vol.58 (4), p.344-354
Main Authors: Eryilmaz, Serkan, Koutras, Markos V., Triantafyllou, Ioannis S.
Format: Article
Language:English
Subjects:
Exchange
exchangeable distribution
Logistics
m-consecutive-k-out-of-n: F system
Mathematical analysis
Mathematical models
mean residual lifetime
Naval
order statistics
Samaniego's signature
Signatures
Statistics
stochastic ordering
Survival
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Summary:In this article, we study reliability properties of m‐consecutive‐k‐out‐of‐n: F systems with exchangeable components. We deduce exact formulae and recurrence relations for the signature of the system. Closed form expressions for the survival function and the lifetime distribution as a mixture of the distribution of order statistics are established as well. These representations facilitate the computation of several reliability characteristics of the system for a given exchangeable joint distribution or survival function. Finally, we provide signature‐based stochastic ordering results for the system's lifetime and investigate the IFR preservation property under the formulation of m‐consecutive‐k‐out‐of‐n: F systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011
ISSN:0894-069X
1520-6750
1520-6750
DOI:10.1002/nav.20449