We consider the component testing problem of a device that is designed to perform a mission consisting of a sequence of stages. Once a stage is over, the device is overhauled to replace all failed components before the next stage starts to improve mission reliability. The components fail exponentially where the failure rate depends on the stage of the mission. The reliability structure of the device involves a series connection of redundant subsystems. The optimal component testing problem is formulated as a semi-infinite linear programme. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it with numerical results.