Development of a new general class of bivariate distributions based on reversed hazard rate order

Motivated by real data sets to be analyzed in this paper, we develop a new general class of bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’ in a system with two components based on the reversed hazard rate. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. In the developed class of bivariate distributions, it is assumed that the residual lifetime of the remaining component is shortened according to the reversed hazard rate order. We derive the joint survival function, joint probability density function and the marginal distributions. We discuss a bivariate ageing property of the developed class of distributions. Some specific families of bivariate distributions which can be usefully applied in practice are obtained. These families of bivariate distributions are applied to some real data sets to illustrate their usefulness.