Component testing of a series system in a random mission

Components of a series system are tested in order to assure desired levels of system reliability during the mission. The components are nonidentical but they all fail exponentially with failure rates that depend on the mission performed. There is a given set of missions that the device can be assigned randomly with respect to a given probability distribution. This directly implies that the failure rates of the components depend on the specific mission that the device performs. The objective is to find an optimal component test plan. We will show that, with some extra effort, this rather complicated but realistic model can be handled using available results in semi-infinite linear programming and d.c. (difference of convex functions) programming.