Reliability studies of bivariate distributions with exponential conditionals

In this paper, we study two bivariate distributions having exponential conditionals. In one of the models, the conditioning variable is fixed and in the other it exceeds a fixed value. We study these two models from a reliability point of view. Failure rates and the mean residual life functions of the marginal distributions and their monotonic properties are studied. The hazard components and their properties are investigated and their relationships with some measure of dependence are established. Finally, the failure rate of the minimum of two components is examined and its monotonicity is investigated. Some of the results presented here are general and would be useful in studying the dependence structure in other classes of bivariate distributions.