Univariate Extreme Shock Maintenance Model for a Repairable System Under Alpha Series Process.

Abstract

In this paper, univariate extreme shock maintenance model for a repairable system under Alpha series process. Assume that the shocks from the system environment. A shock is called a deadly shock, if the amount of damage of one shock to the system exceeds a specific threshold so that the system will fail. For a deteriorating system, we assume that the successive threshold values are non-decreasing after repair, and the consecutive repair times after failure form an increasing Alpha series process. For an improving system, we assume that the successive threshold values are decreasing after repair, and the consecutive repair times after failure form a decreasing Alpha series process. A replacement policy  is adopted by which we shall replace the system by an identical new one at the time following the -th failure. Then for each of the deteriorating system and improving system, an explicit expression for the long run average cost per unit time under  policy is derived and an optimal policy  for minimizing the long run average cost per unit time is determined analytically. A numerical example is given for deteriorating system.