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

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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.

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Authors and Affiliations

  1. Dipartimento di Economia e Statistica, Università della Calabria, via Bucci, cubo 0C, Arcavacata di Rende, CS, Italy

    Filippo Domma & Sabrina Giordano

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  1. Filippo Domma
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  2. Sabrina Giordano
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Correspondence to Sabrina Giordano.

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Domma, F., Giordano, S. A copula-based approach to account for dependence in stress-strength models. Stat Papers 54, 807–826 (2013). https://doi.org/10.1007/s00362-012-0463-0

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  • DOI: https://doi.org/10.1007/s00362-012-0463-0

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