Robust design for the primary suspension of a railway vehicle was performed according to the optimization of 10 dynamic responses representing driving safety and ride comfort, in which response surface models (RSMs) from the design of experiments (DOEs) were applied. To evaluate the probabilistic feasibility of robustness, an intensive computational process is mandatory. In the present study, the authors utilized the first-order Taylor series expansion to reduce the computational burden associated with a probabilistic feasibility evaluation, thus easily obtaining both an individual mean and variance of constraints. To overcome the difficulty of optimizing the mean and probabilistic variances for the 10 dynamic responses, a process capability index ($C_{pk}$) was introduced, which shows the mean value and scattering of the product quality to a certain extent and normalizes the objective functions irrespective of varying dimensions. Consequently, the robust design to optimize the 10 dynamic responses minimized the $C_{pk}$ subjected to the constraint of $C_{pk}$${geq}2$, which satisfied $6{sigma}$. The proposed method improved the $C_{pk}$ that violated the constraints obtained by the RSMs from DOEs and minimized the variance of the $C_{pk}$.