Reliability characteristics of Farlie–Gumbel–Morgenstern family of bivariate distributions

Abstract

In this paper, we study the Farlie–Gumbel–Morgenstern family of bivariate distributions from a reliability point of view. The properties of this family of distributions and the association between the two variables are investigated by studying the local dependence function and the association measure defined by Clayton (1978). We also study the effect of the association parameter on the hazard components, the failure rate of the series system, and the regression mean residual life of a parallel system. Stochastic comparisons with respect to the association parameter are also studied. Some examples are provided to illustrate the results.