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The paper presents a method for obtaining an optimal reliability allocation of an n-stage series system. In each stage, redundant comnponents can be added (in parallel, stand-by, or k-out-of-n:G, etc.), or a more reliable component can be used in order to improve the system reliability. The solution is obtained by repeatedly using a more reliable candidate at each stage that has the greatest value of a `weighted sensitivity function'. The balance between the objective unction and the constraints is controlled by a `balancing coefficient'. The overall computational procedure is given and an example is presented. The computations are given for a set of randomly generated test problems in which the optimal parallel redundancy under linear onstraints is determined. The proposed method is then compared with other methods.