Sensitivity analysis identifies the influential parameters and it is a key step in the design process. Focusing on reliability based design, the probability of a failure mode and its sensitivity to input uncertainties are obtained in a single Monte Carlo simulation using the Likelihood Ratio method. For correlated multiple failure modes, a sensitivity matrix is proposed. The dominant singular vectors of the sensitivity matrix are found to indicate the most important parameters for combined sensitivity of multiple failure modes. Therefore, the sensitivity matrix can guide resources allocation so that most uncertainties can be reduced for system reliabilities.