Extracted reliability information is universal in practice and makes it difficult to estimate system lifetime distributions and reliability. In order to address this problem, this paper develops a method to compute lifetime distributions of serial, parallel, and serial/parallel systems using the failure probability density functions of outsourced components, and then to compute system reliability and component importance measures. Time-varying weights are introduced to simplify the lifetime distribution of a system with multiple types of components and make the system lifetime distribution to be a sum of component probability density functions. A case study illustrates the developed method by identifying the lifetime distribution of a radio navigation system for large passenger aircraft. To demonstrate the effectiveness of the developed method, the estimation results from the developed method are compared with the results from a computer simulation method.