The Roots of the Reliability Polynomials of Circular Consecutive- k -out-of- n:F Systems

Marilena Jianu (), Leonard Dăuş, Vlad-Florin Drăgoi and Valeriu Beiu
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Marilena Jianu: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
Leonard Dăuş: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
Vlad-Florin Drăgoi: Department of Mathematics and Computer Science, Faculty of Exact Sciences, “Aurel Vlaicu” University of Arad, 310330 Arad, Romania
Valeriu Beiu: Department of Mathematics and Computer Science, Faculty of Exact Sciences, “Aurel Vlaicu” University of Arad, 310330 Arad, Romania

Mathematics, 2023, vol. 11, issue 20, 1-12

Abstract: The zeros of the reliability polynomials of circular consecutive- k -out-of- n :F systems are studied. We prove that, for any fixed k ≥ 2 , the set of the roots of all the reliability polynomials (for all n ≥ k ) is unbounded in the complex plane. In the particular case k = 2 , we show that all the nonzero roots are real, distinct numbers and find the closure of the set of roots. For every n ≥ k , the expressions of the minimum root and the maximum root are given, both for circular as well as for linear systems.

Keywords: consecutive- k -out-of- n :F systems; reliability polynomial; Beraha–Kahane–Weiss theorem; Fibonacci polynomials; Jacobsthal polynomials; Lucas polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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