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

作者：Domma Filippo; Giordano Sabrina^*

来源：Statistical Papers, 2013, 54(3): 807-826.

DOI：10.1007/s00362-012-0463-0

• Reliability
• Burr distributions
• Kendall%26apos
• s tau
• Farlie-Gumbel-Morgenstern copula
• Frank copula

The focus of stress-strength models is on the evaluation of the probability R = P(Y %26lt; 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%26apos;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.

• 出版日期2013-8