A system accumulates wear λ(t) at a constant rate and is subject to shocks. The shock arrival process is an inhomogeneous Poisson process with intensity function λ(t) and at each of the instants of shock, a general repair brings down the damage λ(t) by a constant amount. The optimal time for replacement of the system is obtained by using the long-run expected cost per unit time. In view of the difficulties in obtaining the distribution of the shock counting process N ( t ), various monotonicity properties of the “virtual age” process and the counting process N ( t ) with respect to the stochastic ordering of general repairs, for a more general age-dependent shock model are obtained.
