You measure how much stress is applied to critical components, which uses up some of their finite lives. From experiment and theory, we know how much "damage" is done to a part subjected to a given stress. Similarly we know how much stress on components is generated in each launch. Therefore we can take the total life of each critical part (determined thru experiment and analysis), and divide it by the reduction in life (= damage) for each launch, to get the number of remaining launches. The part with the lowest remaining life determines the life of the system.