A copula-based approach to account for dependence in stress-strength models

Filippo Domma () and Sabrina Giordano ()

Statistical Papers, 2013, vol. 54, issue 3, 807-826

Abstract: The focus of stress-strength models is on the evaluation of the probability R = P(Y > X) that stress Y experienced by a component does not exceed strength X required to overcome it. In reliability studies, X and Y are typically modeled as independent. Nevertheless, in many applications such an assumption may be unrealistic. This is an interesting methodological issue, especially as the estimation of R for dependent stress and strength has received only limited attention to date. This paper aims to fill this gap by evaluating R taking into account the association between X and Y via a copula-based approach. We calculate a closed-form expression for R by modeling the dependence through a Farlie-Gumbel-Morgenstern copula and one of its extensions, numerical solutions for R are, instead, provided when members of Frank’s copula family are employed. The marginal distributions are assumed to belong to the Burr system (i.e. Burr III, Dagum or Singh-Maddala type). In all the cases, we prove that neglect of the existing dependence leads to higher or lower values of R than is the case. Copyright Springer-Verlag 2013

Keywords: Reliability; Burr distributions; Kendall’s tau; Farlie-Gumbel-Morgenstern copula; Frank copula (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s00362-012-0463-0

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