On the bivariate modeling of reliability systems: Some advances

Abstract

In this chapter, we study the reliability characteristics of well-known structures using two components. More precisely, we consider different bivariate distribution models such as the Freund's family or the Gumbel Type III family and shed light on several reliability attributes of series and parallel systems. Among other general results, we derive closed formulae for evaluating the reliability function, the mean residual lifetime, or the failure rate of the aforementioned reliability structures. Several figure-based remarks are pointed out, while some open issues referring to the bivariate reliability models are also highlighted. © 2021 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.