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.
A copula-based approach to account for dependence in stress-strength models / Domma, Filippo; Giordano, Sabrina. - In: STATISTICAL PAPERS. - ISSN 0932-5026. - 54:3(2013), pp. 807-826.
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|Titolo:||A copula-based approach to account for dependence in stress-strength models|
|Data di pubblicazione:||2013|
|Citazione:||A copula-based approach to account for dependence in stress-strength models / Domma, Filippo; Giordano, Sabrina. - In: STATISTICAL PAPERS. - ISSN 0932-5026. - 54:3(2013), pp. 807-826.|
|Appare nelle tipologie:||1.1 Articolo in rivista|