Components of electromechanical systems usually contain multiple performance parameters and degrade over time. In previous studies, the reliability of these electromechanical systems was analyzed by the traditional method, and the system reliability was estimated based on the reliability of components and the structures of the systems. The system reliability estimated by the traditional method could not reflect the performance of the systems. A new method is proposed in this paper to analyze the system reliability according to the data of multiple performance degraded processes of components. The performance distribution of a degraded component is obtained by the performance degradation analysis, and then states of the component are defined and corresponding state probabilities are estimated. The universal generating function method is proposed and extended to compute the performance distribution and reliability of the system based on the performances of components. A numerical example illustrates the proposed method. The results of the example show that the proposed method can relate the performance of the system to the performances of components and absolutely reflect the relationship between reliability and performance. Compared with the exact values of the system reliability, the results obtained by the proposed method is almost the same with the exact values, and the results obtained by the traditional method are conservative. The proposed method overcomes the shortcomings of the traditional method and provides a new approach to analyze the reliability of electromechanical systems with degraded components containing multiple performance parameters.