An optimal replacement policy for a two-component series system assuming geometric process repair

This article studies a series repairable system consisting of two non-identical components and one repairer. It is assumed that each component after repair in the system is not “as good as new”. Under this assumption, by using a geometric process repair model, a replacement policy (M,N)(M,N) is considered, based on the number of failures of component 1 and component 2. The problem is to determine an optimal replacement policy (M∗,N∗)(M∗,N∗) such that the long-run expected cost per unit time is minimized. The explicit expression for the long-run expected cost per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some theoretical results included the sensitivity analysis and the uniqueness of the optimal replacement policy (M∗,N∗)(M∗,N∗).