A BIVARIATE OPTIMAL REPLACEMENT POLICY FOR A REPAIRABLE SYSTEM WITH NONN REPAIR TIMES UNDER ALPHA SERIES PROCESS

Abstract

In this paper a bivariate optimal replacement policy for a repairable system consisting of one unit and a single repairman with NONN repair times under Alpha series processe is studied . Assume that the system after repair is not as good as new. Under this assumption, a bivariate optimal replacement policy (T,N), and we consider a replacement policy T is adapted by which the system will be replaced whenever the working age of the system reaches T; another replacement policy N is the number of failures of the system with NONN repair times of the system is studied. Furthermore, The successive survival times of the system after repair form a decreasing Alpha series process or a renewal process while the consecutive repair times of the system consitute an increasing Alpha series process or a renewal process. Our problem is to determine an optimal replacement policy 〖(T,N)〗^*, such that the long run average cost rate of the system is minimized. The explicit expression of the long- run average cost is derived, the corresponding optimal replacement policy can be determined analytically.