The reliability sensitivity analysis of uncertain multi-degree-of-freedom nonlinear vibration systems with independent failure modes subjected to random excitation is examined. An earlier version of the statistical fourth-moment method is extended to deal with vector-valued and matrix-valued functions and is developed to determine the first low moments of the system response and state function. Random variables and system derivatives are conveniently arranged into 2D matrices by means of Kronecker algebra. The distribution function of the system state function is approximately determined by the standard normal distribution functions using Edgeworth series technique, and its reliability and reliability sensitivity are presented and discussed.