Optimal Replacement Policy for two Dissimilar Component Series Repairable System using two Monotone Processes

Abstract

This paper studies a replacement policy (N1, N2) for a series repairable system consisting of two non-identical
components and one repair man. It is assumed that each component after repair in the system is not ‘as good as new‘
and the successive working times form a decreasing  -series process while, the successive repair time’s form an
increasing geometric process and both the processes are exposing to exponential failure law. Under this assumption by
using a monotone process repair model, a replacement policy (N1, N2) based on the number of failures of component 1
and component 2 respectively is considered. An explicit expression for the long run expected cost rate is derived and the
corresponding optimal replacement policy (N*1, N*2) is obtained such that the long run expected cost per unit time is
minimized. Finally, numerical results are provided to highlight the obtained theoretical results. Numerical results are
also exhibited by the graphically.