An Archimedean Copulas-Based Approach for m -Consecutive- k -Out-of- n: F Systems with Exchangeable Components

Ioannis S. Triantafyllou ()
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Ioannis S. Triantafyllou: Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece

Stats, 2023, vol. 6, issue 4, 1-12

Abstract: It is evident that several real-life applications, such as telecommunication systems, call for the establishment of consecutive-type networks. Moreover, some of them require more complex connectors than the ones that exist already in the literature. Thereof, in the present work we provide a signature-based study of a reliability network consisting of identical m -consecutive- k -out-of- n : F structures with exchangeable components. The dependency of the components of each system is modeled with the aid of well-known Archimedean copulas. Exact formulae for determining the expected lifetime of the underlying reliability scheme are provided under different Archimedean copulas-based assumptions. Several numerical results are carried out to shed light on the performance of the resulting consecutive-type design. Some thoughts on extending the present study to more complex consecutive-type reliability structures are also discussed.

Keywords: m -consecutive- k -out-of- n : F systems; Clayton copula model; Gumbel–Hougaard copula model; maximal signature; exchangeable components (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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