Optimal Replacement Model for a Deteriorating System under Partial Sum Process

Abstract

In this paper, the maintenance model for a deteriorating system under partial sum process is studied. Whenever a failure arrives, the system operating time is reduced. Assuming that successive operating times after repairs form a decreasing Partial Sum Process and also consecutive repair times of the system after failures form an increasing Geometric Process, a replacement policy  by which we replace the system whenever the working age of the system reaches  is adopted. An explicit expression for the long run average cost rate per unit per unit time is derived. Optimality conditions are deduced. Numerical illustration is included to strengthen the theoretical results devolved.