A geometric process repair model for a series repairable system with k dissimilar components

In this paper, a geometric process repair model for a k-dissimilar-component series repairable system with one repairman is proposed. For each component, the successive operating times form a decreasing geometric process whereas the consecutive repair times constitute an increasing geometric process. Under this assumption, we consider a replacement policy M = (N1, N2, … , Nk) based respectively on the number of failures of component 1, component 2, …, and component k  . Our problem is to determine an optimal replacement policy M∗=(N1∗,N2∗,…,Nk∗) such that the average cost rate (i.e. the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some issues included the sensitivity analysis and the uniqueness of the optimal replacement policy M∗.