An approximation to the steady state probabilities of a multi-echelon repair model for a series system

A multi-echelon repair system is often employed for the repair of a complex device. There have been many papers on a multi-echelon repair system. Most of them, however, treat the case that i) the repair system has one central repair station(two-echelon repair model), ii)the device is a single item system. The purpose of this paper is to extend a two-echelon repair model with single item systems to a multi-echelon repair model with multi-item systems. This extension makes the repair model more realistic. Then an approximation method to obtain the steady state probabilities of the repair model is presented. This method obtains the probabilities rapidly and accurately. The reliability measure considered in this model is the system availability. It is obtained as a byproduct of the steady state probabilities.