SOME RESULTS ON THE LIFE DISTRIBUTION PROPERTIES OF SYSTEMS SUBJECT TO SHOCKS AND GENERAL REPAIR

A system accumulates wear lambda(t) at a constant rate and is subject to shocks. The shock arrival process is an inhomogeneous Poisson process with intensity function lambda(t) and at each of the instants of shock, a general repair brings down the damage lambda(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.