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In this paper, we study the joint distribution of the backward and forward recurrence times in a renewal process, from the reliability point of view. The survival function, the failure rate, and the mean residual life function, are derived, and their monotonicity is discussed for the marginals, as well as the conditional models. We derive a time dependent association measure in terms of the hazard gradient, and its value, in the case of the model under consideration, is obtained. A real-life application is included to illustrate the importance of the model.