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Dynamic programming value iteration is made more efficient on a five-machine unreliable series line by characterizing the transient and "insensitive" states. Holding costs are minimized subject to a service level constraint in a make-to-stock system with backordering. State-space truncations are chosen by checking the recurrent class in previous runs. An approximate model is developed that reduces the number of machine states. Monotone control theory is used to restrict the search for a control switching surface. Numerical optimal policies are compared with the heuristic control point policy and several characteristics of optimal policies are identified.