We consider the component testing problem of a system that has to perform a mission consisting of a sequence of stages. Once a stage is over, all failed components of the system are replaced before the next stage starts in order to improve its reliability. The components have exponential life distributions where the failure rates depend on the stage of the mission. We formulate the optimal component testing problem as a semi-infinite linear program. We present an algorithmic procedure to compute optimal test times based on the column generation technique and illustrate with numerical examples. (c) 2007 Elsevier B.V. All rights reserved.