In electronic vehicles (EVs) or hybrid electronic vehicles (HEVs), an inverter system has a direct-current-link capacitor (DC-link capacitor) which provides reactive power, attenuates ripple current, reduces the emission of electromagnetic interference, and suppresses voltage spikes. A film capacitor has been used as the DC-link capacitor in high level power system, but the film capacitor's performance has deteriorated over operating time. The decreasing performance of the film capacitor may cause a problem when supplying and delivering energy from the battery to the vehicle's power system. Therefore, the lifetime prediction of the film capacitor could be one of critical factors in the EVs and HEVs. For this reason, the lifetime and reliability of the film capacitor are key factors to show the stability of the vehicle inverter system. There are a lot of methods to predict the lifetime of the film capacitor. Those methods have been researched include using physical or chemical equations. However, these previous researches have a problem with robustness with respect to uncertainty. In this paper, a new prediction model is proposed for the lifetime and stability of the film capacitor which is guaranteed by stochastic methods. Capacitance loss is introduced and modeling of two types of capacitance loss. The parameters of each model are obtained by using curve fitting algorithm and Expectation-Maximization algorithm (EM algorithm). Comparing the predicting result and the real experiment result shows that the new proposed prediction model gives a good performance.