Mathematical Modelling of System Lifetimes Under Cascading Effect and Dependence

Abstract: In this paper, we discuss the lifetimes of systems composed of components having interdependence and cascading effect. For this, a class of bivariate distributions is constructed based on the notion of conditional failure rate. We show that the members in a suitably defined subclass of the developed bivariate distributions satisfy the bivariate lack of memory property. Based on the developed class of distributions, we study the lifetimes of systems having interdependence and cascading effect. We compare the lifetimes of systems having interdependence and cascading effect with those of systems having independent components. The obtained results can be usefully applied to civil engineering.