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

Content Provider	Springer Nature Link
Author	Domma, Filippo Giorda, Sabrina
Copyright Year	2012
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.
Starting Page	807
Ending Page	826
Page Count	20
File Format	PDF
ISSN	09325026
Journal	Statistical Papers
Volume Number	54
Issue Number	3
e-ISSN	16139798
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-08-09
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Reliability Burr distributions Kendall’s tau Farlie-Gumbel-Morgenstern copula Frank copula Statistics for Business/Economics/Mathematical Finance/Insurance Probability Theory and Stochastic Processes Economic Theory Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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