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

• Published in: Stats (Basel, Switzerland) Vol. 6; no. 4; pp. 1114 - 1125
• Main Author: Triantafyllou, Ioannis S.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2023
• Subjects: Clayton copula model; exchangeable components; Gumbel–Hougaard copula model; Lifetime; m-consecutive-k-out-of-n: F systems; maximal signature; Random variables
• ISSN: 2571-905X; 2571-905X
• DOI: 10.3390/stats6040070

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.