We consider the problem of optimizing component testing for a series system with redundant subsystems so as to minimize the total cost of testing given the requirements: the probability of accepting the system must be less than α if the system reliability is less thanR0, and the probability of rejecting the system must be less than β if the system reliability is greater thanR1. This problem was solved previously for a series system under the acceptance criterion that the total number of test failures is less than a prescribed numberk. That result is extended in this paper to cover the more general case of a series system that has built-in redundancy in that it consists of subsystems each of which contains several identical components in parallel. The optimum value ofkand the associated component testing times which will satisfy the above probability requirements are obtained. These requirements can be guaranteed only ifR1is larger than a value that depends onR0. The optimum testing time is shown to be independent of the individual component testing costs.