Renewal convergence rates for DHR and NWU lifetimes

This article studies the geometric convergence rate of a discrete renewal sequence with decreasing hazard rate or, more generally, new worse than used lifetimes. Several variants of these structural orderings are considered. The results are derived from power series methods; roots of generating functions are the prominent issue. Optimality of the rates are considered. Examples demonstrating the utility of the results, as well as applications to Markov chains, are presented.