Redundancy Allocation for Serial Systems

The availability of advanced technical systems (e.g. material handling systems, defense systems, manufacturing systems, computer networks) are crucial as they are used in core processes by their users. Designing systems with redundancy and repairing them by replacing failed parts (repair-by-replacement) during the exploitation phase are common practices to meet a high availability target. Spare parts are kept on stock at a short distance of the installed systems to realize the repair-by-replacement concept efficiently. We introduce a model for redundancy optimization of a system which is composed of subsystems placed in a serial structure. At most two identical, repairable parts can be used in a cold standby redundancy setting in each subsystem. We investigate a situation in which a user buys a number of units of this system. The systems are supported by a single spare parts inventory stock point. A defined emergency procedure is performed in out-of-stock or almost-out-of-stock situations. Redundancy and spare parts inventory level per subsystem are the decision variables in the model. We formulate the problem as the minimization of the Total Cost of Ownership (TCO) of a general number of systems under a certain availability constraint. We conduct exact analysis and derive a number of analytical properties which characterize the optimal spare parts inventory level and redundancy on subsystem level. We provide a system-level rule for ordering the subsystems for redundancy.