As the power density of modern electronic circuits increases dramatically, systems are prone to overheating. High temperatures not only raise packaging costs, degrade system performance, and increase leakage power consumption, but also reduce the system reliability. Due to many limits in single core design including the performance and the power density, the microprocessor industry has switched their attentions to multicore design to enable the scaling of performance. Thermal effects on multicore systems are still prominent issues. One typical thermal effect is the thermal-aware lifetime reliability, which has become a serious concern. In this paper, we address the issue on how to maximize the lifetime of multicore systems while maintaining a given aggregate processor speed. By applying sequential quadratic programming, we present how to derive the ideal speed for each core to maximize the system lifetime. We perform experiments on several multi-core platforms, which show that the proposed method can significantly outperform the existing approaches by minimizing the peak temperature of the system.