Integral optimization of spare parts inventories in systems with redundancies

In this paper, we analyze spare parts supply for a system with a "k-out-of-N" redundancy structure for key components, different standby policies (cold, warm and hot standby redundancy) and local spare parts inventories for sub-components. We assume multiple part types (sub-components) that fail randomly with exponentially distributed interfailure times. Due to the standby policies and the limited number of installed components, the total failure rate depends on the state of the system. Replacement times and stock replenishment times are also assumed to be exponentially distributed and depend on the part types. We present an exact method together with a simple and effi�cient approximation scheme for the evaluation of the system availability given certain stock levels. The proposed approximation is further used in a simple optimization heuristic to demonstrate how the total system costs can be reduced if the redundancy structure is optimized while taking into account the local stock of the spare parts. The presented numerical results clearly show the importance of the local inventories with spares even in the systems with redundancies.