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The paper considers a series system consisting of n components with constant failure rates and obtains a component testing procedure of minimum cost such that a) the probability of accepting a system whose reliability is less than R0 is less than Â¿, and b) the probability of rejecting a system whose reliability is greater than R1 is less than Ã. A decision rule is used that accepts the system if and only if the number of component failures does not exceed k, where k is a given integer. The optimum value of k and the associated component testing times which will satisfy the above probability requirements are obtained. The optimum testing time is the same for each component, irrespective of the individual component testing costs.