Component testing of repairable systems in multistage missions

We consider the component testing problem of a device that is designed to p erform 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 s tage starts to improve mission reliability. The components fail exponential ly where the failure rate depends on the stage of the mission. The reliabil ity structure of the device involves a series connection of redundant subsy stems. The optimal component testing problem is formulated as a semi-infini te linear programme. We present an algorithmic procedure to compute optimal test times based on the column generation technique, and illustrate it wit h numerical results.