The vibration problem of the general system is the main object of research. The material properties and geometry of general system are random parameters because of the manufacturing environment, technical conditions, manufacturing and installation errors, multiphase materials, features and other factors. According to the relation criterion that the difference between the natural frequency and the driving frequency of general systems is not beyond a specific value, the vibration reliability mode and vibration reliability of general systems are defined considering the correlation of the multi-order natural frequency and the random characteristics of structure size and material, and the vibration reliability analysis method for avoiding the resonant is carried out. The second-order joint failure probability is obtained by using the numerical integration method. Based on the reliability design theory and sensitivity analysis method, the vibration reliability sensitivity of the general system with correlation failure modes is extensively discussed and a numerical method for vibration reliability sensitivity design is presented. The variation regularities of vibration reliability sensitivity are obtained and the effects of random parameters on vibration reliability of the general system are studied. The presented method provided the theoretic basis for the reliability design of the general system. A numerical example demonstrated that the proposed method is effective.