On coupling of renewal processes with use of failure rates

AbstractWe construct a coupling of renewal processes by using failure rates; it is particularly useful when the failure rate function of the lifelength distribution is monotone. For the case when that function is decreasing, the speed of convergence towards stationarity of the renewal processes is established, with ease, and a unifying treatment of monotonicity properties of functionals of such processes is given. A relaxed condition for the key renewal theorem is presented. The value of the coupling for the IFR case is discussed briefly